- Assistant Professor of Mechanical and Aerospace Engineering
The Hong Kong University of Science and Technology - +852 3469 2969
- Stanford University, Mechanical Engineering, Post-DocTechnical University of Munich, Mechanical Engineering, Post-Docadd
- I am a Professor in HKUST.edit
A new resolvent-based method is developed to predict the space–time properties of the flow field. To overcome the deterioration of the prediction accuracy with increasing distance between the measurements and predictions in the... more
A new resolvent-based method is developed to predict the space–time properties of the flow field. To overcome the deterioration of the prediction accuracy with increasing distance between the measurements and predictions in the resolvent-based estimation (RBE), the newly proposed method utilizes the RBE to estimate the relative energy distribution near the wall rather than the absolute energy directly estimated from the measurements. Using this extra information from RBE, the new method modifies the energy distribution of the spatially uniform and uncorrelated forcing that drives the flow system by minimizing the norm of the cross-spectral density tensor of the error matrix in the near-wall region in comparison with the RBE-estimated one, and therefore it is named as the resolvent-informed white-noise-based estimation (RWE) method. For validation, three time-resolved direct numerical simulation (DNS) datasets with the friction Reynolds numbers Reτ=180, 550 and 950 are generated, with various locations of measurements ranging from the near-wall region (y+=40) to the upper bound of the logarithmic region (y/h≈0.2, where h is the half-channel height) for the predictions. Besides the RWE, three existing methods, i.e. the RBE, the λ-model and the white-noise-based estimation (WBE), are also included for the validation. The performance of the RBE and scale-dependent model (λ-model) in predicting the energy spectra shows a strong dependence on the measurement locations. The newly proposed RWE shows a low sensitivity on Reτ and the measurement locations, which may range from the near-wall region to the upper bound of the logarithmic region, and has a high accuracy in predicting the energy spectra. The RWE also performs well in predicting the space–time properties in terms of the correlation magnitude and the convection velocity. We further utilize the new method to reconstruct the instantaneous large-scale structures with measurements from the logarithmic region. Both the RWE and RBE perform well in estimating the instantaneous large-scale structure, and the RWE has smaller errors in the estimations near the wall. The structural inclination angles around 15∘ are predicted by the RWE and WBE, which generally recover the DNS results.
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While the recently proposed TENO (targeted essentially non-oscillatory) schemes [Fu et al., Journal of Computational Physics 305 (2016): 333-359] exhibit better performance than the classical WENO (weighted essentially non-oscillatory)... more
While the recently proposed TENO (targeted essentially non-oscillatory) schemes [Fu et al., Journal of Computational Physics 305 (2016): 333-359] exhibit better performance than the classical WENO (weighted essentially non-oscillatory) schemes with the same accuracy order, there is still a room for further improvement, e.g., the physical discontinuities may be significantly smeared by the excessive numerical dissipation due to the enforcement of the ENO property after a long-time advection. More recently, a new fifth-order TENO5-THINC scheme is proposed by coupling the TENO5 scheme with a non-polynomial THINC (tangent of hyperbola for interface capturing) scheme based on a parameter-free discontinuity indicator. The novelty originates from the fact that the new strategy locates the discontinuities accurately and deploys the jump-like THINC reconstruction scheme for resolving the discontinuities with a sub-cell resolution, instead of enforcing the ENO property. The new scheme successfully leverages the excellent wave-resolution property of standard TENO schemes for smooth and under-resolved continuous scales and the discontinuity-resolving capability of THINC for reconstructing genuine discontinuities. In this work, we further develop the low-dissipation discontinuity-resolving very-high-order TENO-THINC reconstruction schemes for hyperbolic conservation laws by proposing tailored coupling strategies. Without loss of generality, the six-and eight-point TENO-THINC schemes are developed, and the explicit formulas are given as well as the built-in parameters.
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Linear models, based on stochastically-forced linearized equations, are deployed for spectral linear stochastic estimation (SLSE) of the velocity and temperature fluctuations in compressible turbulent channel flows with a bulk Mach number... more
Linear models, based on stochastically-forced linearized equations, are deployed for spectral linear stochastic estimation (SLSE) of the velocity and temperature fluctuations in compressible turbulent channel flows with a bulk Mach number of 1.5. Through comparing with the direct numerical simulation (DNS) data, an eddy-viscosity-enhanced model (eLNS) outperforms the one not enhanced (LNS) in computing the coherence and amplitude ratio of streamwise velocity at different wall-normal heights, but they both largely deviate from DNS regarding the temperature prediction. For further investigation, the eigenspectra and pseudospectra of the linear operators are scrutinized. The eddy viscosity is shown to damp the eigenmodes and decrease the non-normality of the vortical modes. Consequently, the relative importance of acoustic and entropy modes increases, and they can contribute 20% to 55% of the response growth, which is not supported by DNS. Hence, it is an intrinsic defect of the eLNS model introduced by turbulence modelling. After a procedure of cospectrum decomposition, the contributions of acoustic and entropy components are filtered out. The resulting SLSE quantities for velocity, temperature and their coupling are basically agreeable with DNS, demonstrating that the coherent temperature fluctuation is dominated by advection and other vortical motions, instead of the compressibility effects. Moreover, a parameter study of Reynolds and Mach numbers (from 0.3 to 4) is conducted. It is shown that the semi-local units well collapse the velocity SLSE quantities to the incompressible case for streamwise-elongated structures of high coherence.
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Particle shifting technique (PST) in smoothed particle hydrodynamics (SPH) is a useful strategy to render particle distribution isotropic for higher numerical accuracy and stability. However, the non-isotropic particle distribution near... more
Particle shifting technique (PST) in smoothed particle hydrodynamics (SPH) is a useful strategy to render particle distribution isotropic for higher numerical accuracy and stability. However, the non-isotropic particle distribution near the free surfaces and volume non-conservation still often occur, which will degenerate accuracy in the long-time simulation with violent flows. In this study, the two major concerns are solved by proposing a new PST. The Voronoi cell is constructed for the particles with incomplete kernel support, and the difference between the Voronoi cell centroid and the corresponding particle location is used to determine the shifting vector, which ensures a very isotropic particle distribution and that no clustering or nonphysical gap occurs in these areas. For the free-surface particles, the shifting vector is determined according to the volume change and thus the volume conservation is ensured, where the volume is calculated conveniently with the merit of Voronoi diagram. The present method is compared with the other two advanced PST methods, and a set of challenging cases with violent flows is simulated to validate its superior properties in terms of maintaining isotropic particle distribution and volume conservation. Moreover, the efficiency of the present method is almost the same as those of other advanced PSTs. Overall, the new PST method presents a strong potential in the long-time simulation of violent flows in coastal engineering.
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In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation (Griffin et al., Proc. Natl Acad. Sci., vol. 118, 2021, p. 34) and an algebraic temperature-velocity relation, is... more
In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation (Griffin et al., Proc. Natl Acad. Sci., vol. 118, 2021, p. 34) and an algebraic temperature-velocity relation, is developed for high-speed turbulent boundary layers. As input, the model requires the mean flow state at one wall-normal height in the inner layer of the boundary layer and at the boundary-layer edge. As output, the model can predict mean temperature and velocity profiles across the entire inner layer, as well as the wall shear stress and heat flux. The model is tested in an a priori sense using a wide database of direct numerical simulation high-Mach-number turbulent channel flows, pipe flows and boundary layers (48 cases, with edge Mach numbers in the range 0.77-11, and semi-local friction Reynolds numbers in the range 170-5700). The present model is significantly more accurate than the classical ordinary differential equation (ODE) model for all cases tested. The model is deployed as a wall model for large-eddy simulations in channel flows with bulk Mach numbers in the range 0.7-4 and friction Reynolds numbers in the range 320-1800. When compared to the classical framework, in the a posteriori sense, the present method greatly improves the predicted heat flux, wall stress, and temperature and velocity profiles, especially in cases with strong heat transfer. In addition, the present model solves one ODE instead of two, and has a computational cost and implementation complexity similar to that of the commonly used ODE model.
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For compressible flow simulations involving both turbulence and shockwaves, the competing requirements render it challenging to develop high-order numerical methods capable of capturing the discontinuities sharply and resolving the... more
For compressible flow simulations involving both turbulence and shockwaves, the competing requirements render it challenging to develop high-order numerical methods capable of capturing the discontinuities sharply and resolving the turbulence with high spectral resolution. In particular when deployed with the advanced large-eddy simulation (LES) approach, for which the governing equations are solved with coarse meshes, the solution is extraordinarily sensitive to the numerical dissipation resulting in large uncertainties for cross-code comparisons. Similar sensitivities have also been observed for a wide range of complex fluid predictions, e.g., turbulent reacting flows, two-phase flows, and transitional flows. In this paper, the family of high-order targeted essentially non-oscillatory (TENO) schemes on both the Cartesian and unstructured meshes is reviewed for general hyperbolic conservation laws with an emphasis on the high-speed turbulent flows. As a novel variant of popular weighted ENO (WENO) scheme, the TENO scheme retains the sharp shock-capturing capability of WENO and is suitable for resolving turbulence with controllable low numerical dissipation. The key success of TENO relies on a strong scaleseparation procedure and the tailored novel ENO-like stencil selection strategy. In addition, the built-in candidate stencils with incremental width facilitate the construction of arbitrarily high-order (both odd-and even-order) schemes featuring superior robustness. Detailed performance comparisons between the WENO and TENO schemes are discussed comprehensively as well as the applications of TENO schemes to challenging compressible fluids. At last, the potential future developments to further boost the performance of TENO schemes from various perspectives are highlighted.
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Particle shifting technique (PST) in smoothed particle hydrodynamics (SPH) is a useful strategy to render particle distribution isotropic for higher numerical accuracy and stability. However, the non-isotropic particle distribution near... more
Particle shifting technique (PST) in smoothed particle hydrodynamics (SPH) is a useful strategy to render particle distribution isotropic for higher numerical accuracy and stability. However, the non-isotropic particle distribution near the free surfaces and volume non-conservation still often occur, which will degenerate accuracy in the long-time simulation with violent flows. In this study, the two major concerns are solved by proposing a new PST. The Voronoi cell is constructed for the particles with incomplete kernel support, and the difference between the Voronoi cell centroid and the corresponding particle location is used to determine the shifting vector, which ensures a very isotropic particle distribution and that no clustering or nonphysical gap occurs in these areas. For the free-surface particles, the shifting vector is determined according to the volume change and thus the volume conservation is ensured, where the volume is calculated conveniently with the merit of Voronoi diagram. The present method is compared with the other two advanced PST methods, and a set of challenging cases with violent flows is simulated to validate its superior properties in terms of maintaining isotropic particle distribution and volume conservation. Moreover, the efficiency of the present method is almost the same as those of other advanced PSTs. Overall, the new PST method presents a strong potential in the long-time simulation of violent flows in coastal engineering.
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We develop a new methodology to assess the streamwise inclination angles (SIAs) of the wall-attached eddies populating the logarithmic region with a given wall-normal height. To remove the influences originating from other scales on the... more
We develop a new methodology to assess the streamwise inclination angles (SIAs) of the wall-attached eddies populating the logarithmic region with a given wall-normal height. To remove the influences originating from other scales on the SIA estimated via twopoint correlation, the footprints of the targeted eddies in the vicinity of the wall and the corresponding streamwise velocity fluctuations carried by them are isolated simultaneously, by coupling the spectral stochastic estimation with the attached-eddy hypothesis. Datasets produced with direct numerical simulations spanning ∼ (10 2) − (10 3) are dissected to study the Reynolds-number effect. The present results show, for the first time, that the SIAs of attached eddies are Reynolds-number dependent in low and medium Reynolds numbers and tend to saturate at 45 • as the Reynolds number increases. The mean SIA reported by vast previous experimental studies are demonstrated to be the outcomes of the additive effect contributed by multi-scale attached eddies. These findings clarify the long-term debate and perfect the picture of the attached-eddy model.
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The multi-resolution method, e.g., the Adaptive Particle Refinement (APR) method, has been developed to increase the local particle resolution and therefore the solution quality within a pre-defined refinement zone instead of using a... more
The multi-resolution method, e.g., the Adaptive Particle Refinement (APR) method, has been developed to increase the local particle resolution and therefore the solution quality within a pre-defined refinement zone instead of using a globally uniform resolution for Smoothed Particle Hydrodynamics (SPH). However, sometimes, the targeted zone of interest can be varying, and the corresponding topology is very complex, thus the conventional APR method is not able to track these characteristics adaptively. In this study, a novel Block-based Adaptive Particle Refinement (BAPR) method is developed, which is able to provide the necessary local refinement flexibly for any targeted characteristic, and track it adaptively. In BAPR, the so-called activation status of the block array defines the refinement regions, where the transition and activated zones are determined accordingly. A regularization method for the generated particles in the newly activated blocks is developed to render an isotropic distribution of these new particles. The proposed method has been deployed for simulating Fluid-Structure Interaction
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For compressible flows characterized by a wide range of flow length scales and discontinuities, it is still an open challenge to design the optimal schemes, which resolve the small-scale flow structures with low numerical dissipation and... more
For compressible flows characterized by a wide range of flow length scales and discontinuities, it is still an open challenge to design the optimal schemes, which resolve the small-scale flow structures with low numerical dissipation and capture the shock waves without artificial oscillations. In Takagi et al. , a novel TENO5-THINC scheme with the combination of classical TENO5 (fifth-order Targeted Essentially Non-Oscillatory) scheme and the non-polynomial THINC (Tangent of Hyperbola for INterface Capturing) reconstruction has been proposed. Building upon the strategy of isolating discontinuities from smooth and high-wavenumber regions, in the present work, a new very low-dissipation TENO scheme with discontinuity-resolving property is proposed for compressible flow simulations based on three new concepts: (1) an improved discontinuity-detecting criterion is devised based on the TENO weighting strategy, which significantly enhances the discontinuity-detecting accuracy compared to that in TENO5-THINC; (2) A local interpolation-like strategy is proposed to represent the detected discontinuity with subcell resolutions, and this strategy can minimize the numerical dissipation even when compared to the THINC reconstruction scheme; (3) According to the varying sharpness of the discontinuities separated by the discontinuity-detecting indicator, the local interpolation-like strategy is extended with a two-steepness approximation. Specifically, the discontinuities will be classified as genuinely sharp discontinuities and general ones. For the genuinely sharp discontinuities, the interface flux will be estimated by a steeper step-like function with even less numerical dissipation. The resulting scheme maintains the high-order and low-dissipation properties of the TENO scheme for smooth flow scales, while further improving the discontinuity-resolving capability and suppressing the numerical oscillations in the vicinity of discontinuities. A variety of benchmark cases with broadband length scales as well as discontinuities is presented to demonstrate the high wave-resolution property and the sharp shock-capturing capability of the proposed scheme.
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This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will... more
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Press, 1976) are two fundamental models describing the multi-scale turbulence interactions and the organization of energy-containing motions in the logarithmic region of high-Reynolds number wallbounded turbulence, respectively. In this... more
Press, 1976) are two fundamental models describing the multi-scale turbulence interactions and the organization of energy-containing motions in the logarithmic region of high-Reynolds number wallbounded turbulence, respectively. In this paper, by coupling the additive description with the attached-eddy model, the generation process of streamwise wall-shear fluctuations, resulting from wall-attached eddies, is portrayed. Then, by resorting to the inner-outer interaction model, the streamwise wall-shear stress fluctuations generated by attached eddies in a turbulent channel flow are isolated. Direct comparison between the statistics from these two models demonstrates that they are consistent to and complement each other. Meanwhile, we further show that the superpositions of attached eddies follow an additive process strictly by verifying the validity of the strong and extended self similarity. Moreover, we propose a Gaussian model to characterize the instantaneous distribution of streamwise wall-shear stress, resulting from the attached-eddy superpositions. These findings are important for developing an advanced reduced-order wall model.
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This work assesses several popular transformations for the velocity profile through their application to several types of non-canonical compressible wall-bounded turbulent flows. Specifically, this work explores DNS databases of... more
This work assesses several popular transformations for the velocity profile through their application to several types of non-canonical compressible wall-bounded turbulent flows. Specifically, this work explores DNS databases of high-enthalpy boundary layers with dissociation and vibrational excitation, supercritical channel and boundary-layer flows, and adiabatic boundary layers with pressure gradients. The transformations considered include the van Driest [Van Driest, J. Aeronaut. Sci., 18(1951):145-216], Zhang et al. [Zhang et al., Phys. Rev. Lett., 109(2012):054502], Trettel-Larsson [Trettel and Larsson, Phys. Fluids, 28(2016):026102], data-driven [Volpiani et al., Phys. Rev. Fluids, 5(2020):052602], and total-stress-based [Griffin et al., Proc. Natl. Acad. Sci. U.S.A., 118(2021):e2111144118] transformations. The Trettel-Larsson transformation collapses velocity profiles of high-enthalpy temporal boundary layers but not the spatial boundary layers considered. For supercritical channel flows, the Trettel-Larsson transformation also performs well over the entire inner layer. None of the transformations above works for supercritical boundary layers. For all the considered methods, the transformed velocity profiles of boundary layers with weak pressure gradients coincide well with the universal incompressible law of the wall. In summary, all these popular methods fail to deliver uniform performance for non-canonical compressible wall-bounded flows in the logarithmic region, and a more sophisticated version, which accounts for these different physics, is needed. The data-driven and total-stress-based transformations perform well in the viscous sublayer for all the considered flows.
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In [Fu et al., JCP 305(2016): 333-359], a family of high-order targeted ENO (TENO) schemes is proposed. The weighting strategy of TENO either applies a candidate stencil with its optimal weight, or removes its contribution completely when... more
In [Fu et al., JCP 305(2016): 333-359], a family of high-order targeted ENO (TENO) schemes is proposed. The weighting strategy of TENO either applies a candidate stencil with its optimal weight, or removes its contribution completely when it is crossed by discontinuities. This ENO-like stencil selection procedure significantly diminishes the numerical dissipation induced by the nonlinear adaptations of classical WENO schemes. In this paper, the fifth-order TENO scheme is extended to simulate reactive flows in combination with an uncoupled method [1, 2], which splits the reaction source term of detailed chemistry from the flow equations. A set of benchmark cases including the two-dimensional self-sustained detonation is simulated to validate and compare the performance of the fifth-order WENO and TENO schemes. Numerical experiments demonstrate that TENO scheme is robust for simulating chemical reacting flows with using the uncoupled method. In particular, TENO scheme shows better performance in capturing both the shockwaves and the small-scale flow structures, e.g. shear layers and vortices.
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Even for state-of-the-art implicit LES (ILES) methods, where the truncation error acts as physically-motivated subgrid-scale model, simultaneously resolving turbulent and genuine non-turbulent subgrid scales is an open challenge. For the... more
Even for state-of-the-art implicit LES (ILES) methods, where the truncation error acts as physically-motivated subgrid-scale model, simultaneously resolving turbulent and genuine non-turbulent subgrid scales is an open challenge. For the purpose of dealing with non-turbulent subgrid scales, such as shocks, extra sensors, which often are case-dependent, are generally employed. The problem originates in the lack of scale-separation between low-wavenumber resolved-scale regions, high-wavenumber resolved or non-resolved fluctuations, and discontinuities. The targeted ENO (TENO) approach allows for separately designing the dispersive and dissipative truncation error components. Thus it provides a suitable environment to develop an implicit LES model. In this paper, we extend previous work and propose a variant of TENO family scheme [Fu et al., JCP 305 (2016): 333-359], which can separate resolved and nonresolved scales effectively. The novel idea is to propose a nonlinear dissipationcontrol strategy by adapting the cutoff parameter C T dynamically while measuring the nonsmoothness based on the first-order undivided difference. Low-wavenumber smooth scales are handled by an optimized linear scheme while high-wavenumber components, that involve nonresolved fluctuations and discontinuities, are subjected to adaptive nonlinear dissipation. A set of benchmark simulations with a wide range of length-scales and with discontinuities has been conducted without specific parameter adaptation. Numerical experiments demonstrate that the proposed TENO8-A scheme exhibits robust shock-capturing and high wave-resolution properties, and that it is suitable for simulating flow fields that contain isotropic turbulence and shocks. It is a promising alternative to other viable approaches.
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In this work, we aim to develop estimates for the grid-point and time-step requirements for DNS of compressible flows. Although several works have quantified the cost of simulations of incompressible turbulent flows (Chapman 1979; Choi &... more
In this work, we aim to develop estimates for the grid-point and time-step requirements for DNS of compressible flows. Although several works have quantified the cost of simulations of incompressible turbulent flows (Chapman 1979; Choi & Moin 2012; Yang & Griffin 2021), they did not consider how compressibility leads to mean property variations (e.g. density and viscosity), which alters the size of turbulence structures and thus the required grid-point and time-step requirements for simulations. In addition, in
a cold-wall compressible boundary layer, a sharp peak in the temperature profile can form, and the cost of resolving it is also considered. Also considered is the more stringent time-step requirement due to mean property variations.
a cold-wall compressible boundary layer, a sharp peak in the temperature profile can form, and the cost of resolving it is also considered. Also considered is the more stringent time-step requirement due to mean property variations.
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In the future, very-high-Mach-number vehicles flying at low altitudes could play an important role in global transportation (Urzay 2018). By flying at relatively low altitudes, these systems can use ambient atmospheric oxygen for... more
In the future, very-high-Mach-number vehicles flying at low altitudes could play an important role in global transportation (Urzay 2018). By flying at relatively low altitudes, these systems can use ambient atmospheric oxygen for combustion, instead of conventional rockets, which carry their oxidizer in cryogenic tanks, the weight of which substantially reduces the efficiency of such transportation systems. While the thicker atmosphere is good for air-breathing propulsion, it leads to immense aerodynamic heating, which necessitates accurate numerical simulation to design safe and reliable systems. High-speed flows are numerically challenging to simulate due to the formation of shock waves, which are discontinuities in the continuous governing equations (Shu 2009; Pirozzoli 2011; Fu et al. 2021; Griffin et al. 2021), which are governed by hyperbolic conservation laws. In turbulent flows, it is also essential that the methods have very low numerical dissipation as not to artificially suppress turbulence. In addition, numerical robustness, which is the property that the solution remains bounded (does not blow up), is essential. Since the 1980s, many numerical approaches have been developed, such as the artificial viscosity scheme (Von & Richtmyer 1950; Jameson 1994), total variation diminishing scheme (Harten 1983), essentially non-oscillatory (ENO) (Harten et al. 1987) scheme and weighted essentially non-oscillatory (WENO) scheme (Liu et al. 1994). Among these approaches, the WENO scheme has been widely used in both academic and engineering simulations due to the sharp and robust shock-capturing capabilities. However, there are still some drawbacks, e.g., the order-degeneration near critical points, generating excessive numerical dissipation for small-scale structures, and the lack of numerical robustness for very-high-order reconstructions. Improvements for the order degeneration problem include the WENO-M scheme (Henrick et al. 2005) and the WENO-Z scheme (Borges et al. 2008). The numerical dissipation can be reduced by increasing the order of accuracy (Gerolymos et al. 2009), switching between a low-dissipation and a shock-capturing scheme based on a shock senor (the hybrid concept) (Adams & Shariff 1996), and optimizing the spectral properties of the scheme (improving the modified wavenumber) (Lele 1992; Weirs & Candler 1997). For enhancing the robustness of the scheme, Suresh & Huynhb (1997) propose to bound the solution near discontinuities by a monotonicitypreserving limiter. The order-reduction approach (Gerolymos et al. 2009; Titarev & Toro 2004), which recursively resorts to lower-order stencils, is an alternative way to improve the robustness of WENO schemes. However, when the above mentioned numerical approaches are applied to very-high-Mach-number flows with vacuum or near-vacuum regions, e.g., for applications with low density and low pressure, numerical difficulties may occur due to the presence of negative density and pressure. Although these high-order shock-capturing schemes generate entropy solutions for hyperbolic conservation laws (i.e., entropy monotonically increases), in general, they may fail to preserve positivity, which eventually causes the numerical
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This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will... more
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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In this paper, an efficient low-dissipation high-order TENO scheme is proposed for ideal MHD flows. For high computational efficiency, a troubled-cell indicator based on the ENOlike stencil selection strategy in TENO schemes is introduced... more
In this paper, an efficient low-dissipation high-order TENO scheme is proposed for ideal MHD flows. For high computational efficiency, a troubled-cell indicator based on the ENOlike stencil selection strategy in TENO schemes is introduced to isolate the discontinuities from smooth regions. While the high-order linear scheme is adopted for the smooth regions, a low-dissipation TENO scheme is applied for capturing discontinuities detected by the troubled-cell indicator. The case-independent parameters are given based on spectral analysis. Both the governing equations of the ideal MHD and the Hamilton-Jacobi type constrained transport equation for divergence-free condition can be solved by the newly proposed scheme. Since most computational regions are resolved by the linear scheme without expensive characteristic decomposition, flux splitting and nonlinear weight calculation, the proposed scheme is highly efficient. A set of benchmark cases has been simulated to demonstrate the performance of the proposed scheme. Numerical results reveal that remarkable speedup is achieved by the present scheme while the oscillation-free property and the high-order accuracy are preserved.
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Accurate prediction of aerothermal surface loading is of paramount importance for the design of high-speed flight vehicles. In this work, we consider the numerical solution of hypersonic flow over a double-finned geometry, representative... more
Accurate prediction of aerothermal surface loading is of paramount importance for the design of high-speed flight vehicles. In this work, we consider the numerical solution of hypersonic flow over a double-finned geometry, representative of the inlet of an air-breathing flight vehicle, characterized by threedimensional intersecting shock-wave/turbulent boundary layer interaction at Mach 8.3. High Reynolds numbers (Re L ≈ 11.6 × 10 6 based on free-stream conditions) and the presence of cold walls (T w /T • ≈ 0.26) leading to large near-wall temperature gradients necessitate the use of wall-modeled large eddy simulation (WMLES) in order to make calculations computationally tractable. The comparison of the WMLES results with experimental measurements shows good agreement in the time-averaged surface heat flux and wall pressure distributions, and the WMLES predictions show reduced errors with respect to the experimental measurements than prior RANS calculations. The favorable comparisons are obtained using a standard LES wall model based on equilibrium boundary layer approximations despite the presence of numerous non-equilibrium conditions including threedimensionality in the mean, shock/boundary layer interactions, and flow separation. We demonstrate that the use of semi-local eddy viscosity scaling (in lieu of the commonly used van Driest scaling) in the LES wall model is necessary to accurately predict the surface pressure loading and heat fluxes.
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In this paper, a new family of very-high-order TENO schemes with adaptive accuracy order and adaptive dissipation control (TENO-AA) is proposed. The new framework allows for constructing arbitrarily high-order TENO schemes in a unified... more
In this paper, a new family of very-high-order TENO schemes with adaptive accuracy order and adaptive dissipation control (TENO-AA) is proposed. The new framework allows for constructing arbitrarily high-order TENO schemes in a unified paradigm and the yielded nonlinear schemes gradually reduce to low-order reconstructions by judging the smoothness with the ENO-like stencil selection strategy. In order to control the nonlinear numerical dissipation adaptively, the flow scales are first measured by examining the first-order undivided difference and the cutoff constant C T in the TENO weighting strategy is adapted based on the corresponding measurement. With one set of optimal parameters, the newly proposed TENO schemes are designed to deliver excellent performance for predicting highly compressible flows with a wide range of Mach numbers. While the new very-high-order TENO schemes feature good robustness for conventional gas dynamics, the ENO-property is well preserved with the assistant of a positivity-preserving flux limiter for extreme simulations. Without loss of generality, the typical eight-and ten-point TENO-AA schemes are constructed. A set of benchmark simulations are computed to demonstrate the performance of the proposed TENO schemes. c
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In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall is proposed. Unlike existing approaches, the proposed transformation successfully... more
In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall is proposed. Unlike existing approaches, the proposed transformation successfully collapses, without specific tuning, numerical simulation data from fully developed channel and pipe flows, and boundary layers with or without heat transfer. In all these cases, the transformation is successful across the entire inner layer of the boundary layer (including the viscous sublayer, buffer layer, and logarithmic layer), recovers the asymptotically exact near-wall behavior in the viscous sublayer, and is consistent with the near balance of turbulence production and dissipation in the logarithmic region of the boundary layer. The performance of the transformation is verified for compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and friction Reynolds numbers ranging from 200 to 2000. Based on physical arguments, we show that such a general transformation exists for compressible wall-bounded turbulence regardless of the wall thermal condition.
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The classical equilibrium wall model is popular because it is simple to implement in practical applications, and the performance is, in general, satisfactory for high-Reynolds-number wall-bounded turbulence. However, the prediction... more
The classical equilibrium wall model is popular because it is simple to implement in practical applications, and the performance is, in general, satisfactory for high-Reynolds-number wall-bounded turbulence. However, the prediction capability is limited because the damping coefficient $A^+$ does not depend on the flow state. As a result, upon integration, the classical model predicts the same logarithmic intercept even in the presence of strong pressure gradients and low Reynolds numbers. Specifically, the classical models have invoked the constant-stress-layer assumption or developed approximate correlations of the shear stress profile, without making a corresponding adjustment to the eddy viscosity model, to maintain a log law. These choices are in conflict with a wide range of high-fidelity simulation data. The present model is constructed to recover the log law without the need for assumptions about or approximations of the shear stress profile. On the other hand, whereas most classical stress-based wall models assume a universal value for the mixing length damping coefficient $A^+$, the new method correlates $A^+$ with the boundary-layer shape factor $H$ and the friction Reynolds number $Re_\tau$. The proposed correlation of $A^+[H,Re_\tau]$ makes a substantial improvement to the prediction of the velocity profile and the wall shear stress for a large range of Reynolds numbers and pressure gradient conditions. The ODE-based inner model is designed to live in symbiosis with the outer PDE-based solver, which computes the velocity profile in the outer portion of the boundary layer. By feeding these data into the inner wall model, the shape factor and the wall shear stress can be accurately predicted. As a result, the new model incorporates an integral measure of the streamwise and temporal history of the flow and is accurate in non-equilibrium scenarios, while retaining similar computational efficiency as classical equilibrium models.
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In this work, the canonical model of a realistic inlet configuration of any air-breathing hypersonic vehicle is considered (Kussoy & Horstman 1992). The basic configuration consists of two sharp fins mounted on a flat plate. The salient... more
In this work, the canonical model of a realistic inlet configuration of any air-breathing hypersonic vehicle is considered (Kussoy & Horstman 1992). The basic configuration consists of two sharp fins mounted on a flat plate. The salient flow features are characterized as that a hypersonic turbulent boundary layer approaches the two vertical fins generating a crossing shock pattern as well as a separation zone with strong pressure gradient. The objective of the present investigation is to assess the accuracy of the wall modeled LES approach in the context of more complex geometries and complex flow regimes. In particular, emphasis is placed on the ability to predict surface heat fluxes and the complex separation pattern that arises due to the impinging shock structure.
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In this paper, we present a feature-aware SPH method for the concurrent and automated isotropic unstructured mesh generation. Two additional objectives are achieved with the proposed method compared to the original SPH-based mesh... more
In this paper, we present a feature-aware SPH method for the concurrent and automated isotropic unstructured mesh generation. Two additional objectives are achieved with the proposed method compared to the original SPH-based mesh generator (Fu et al., 2019). First, a feature boundary correction term is introduced to address the issue of incomplete kernel support at the boundary vicinity. The mesh generation of feature curves, feature surfaces and volumes can be handled concurrently without explicitly following a dimensional sequence. Second, a two-phase model is proposed to characterize the mesh-generation procedure by a feature-size-adaptation phase and a mesh-quality-optimization phase. By proposing a new error measurement criterion and an adaptive control system with two sets of simulation parameters , the objectives of faster feature-size adaptation and local mesh-quality improvement are merged into a consistent framework. The proposed method is validated with a set of 2D and 3D numerical tests with different complexities and scales. The results demonstrate that high-quality meshes are generated with a significant speedup of convergence.
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While the computation of the boundary-layer thickness is straightforward for canonical equilibrium flows, there are no established definitions for general non-equilibrium flows. In this work, a new method is developed based on a local... more
While the computation of the boundary-layer thickness is straightforward for canonical equilibrium flows, there are no established definitions for general non-equilibrium flows. In this work, a new method is developed based on a local reconstruction of the "inviscid" velocity profile UI [y] resulting from the Bernoulli equation. The boundary-layer thickness δ99 is then defined as the location where U/UI = 0.99, which is consistent with its classical definition for the zero-pressure-gradient boundary layers (ZPGBLs). The new method is parameter free, and can be deployed for both internal and external flows without resorting to an iterative procedure, numerical integration, or numerical differentiation. The superior performance of the new method over various existing methods is demonstrated by applying the methods to laminar and turbulent boundary layers and two flows over airfoils. Numerical experiments reveal that the new method is more accurate and more robust than existing methods, and it is applicable for flows over a wide range of Reynolds numbers.
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In this work, a framework to construct arbitrarily high-order low-dissipation shock-capturing schemes with flexible and controllable nonlinear dissipation for convection-dominated problems is proposed. While a set of candidate stencils of... more
In this work, a framework to construct arbitrarily high-order low-dissipation shock-capturing schemes with flexible and controllable nonlinear dissipation for convection-dominated problems is proposed. While a set of candidate stencils of incremental width is constructed, each one is indicated as smooth or nonsmooth by the ENO-like stencil selection procedure proposed in the targeted essentially non-oscillatory (TENO) scheme [Fu et al., Journal of Computational Physics 305 (2016): 333-359]. Rather than being discarded directly as with TENO schemes, the nonsmooth candidates are filtered by an extra nonlinear limiter, such as a monotonicity-preserving (MP) limiter or a total variation diminishing (TVD) limiter. Consequently, high-order reconstruction is achieved by assembling candidate fluxes with optimal linear weights since they are either smooth reconstructions or filtered ones which feature good non-oscillation property. A weight renormalization procedure as with the standard TENO paradigm is not necessary. This new framework concatenates the concepts of TENO, WENO and other nonlinear limiters for shock-capturing, and provides a new insight to designing low-dissipation nonlinear schemes. Through the adaptation of nonlinear lim-iters, nonlinear dissipation in the newly proposed framework can be controlled separately without affecting the performance in smooth regions. Based on the proposed framework, a family of new six-and eight-point nonlinear schemes with controllable dissipation is proposed. A set of critical benchmark cases involving strong discontinuities and broadband fluctuations is simulated. Numerical results reveal that the proposed new schemes capture discontinuities sharply and resolve the high-wavenumber fluctuations with low dissipation, while maintaining the desired accuracy order in smooth regions.
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The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar boundary layer over a cold wall is addressed using direct numerical simulations (DNS) and wall-modeled large-eddy simulations (WMLES) at different... more
The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar boundary layer over a cold wall is addressed using direct numerical simulations (DNS) and wall-modeled large-eddy simulations (WMLES) at different angles of incidence. At sufficiently high shock-incidence angles, the boundary layer transitions to turbulence via breakdown of near-wall streaks shortly downstream of the shock impinge-ment, without the need of any inflow free-stream disturbances. The transition causes a localized significant increase in the Stanton number and skin-friction coefficient, with high incidence angles augmenting the peak thermomechanical loads in an approximately linear way. Statistical analyses of the boundary layer downstream of the interaction for each case are provided that quantify streamwise spatial variations of the Reynolds analogy factors and indicate a breakdown of the Morkovin's hypothesis near the wall, where velocity and temperature become correlated. A modified strong Reynolds analogy with a fixed turbulent Prandtl number is observed to perform best. Conventional transformations fail at collapsing the mean velocity profiles on the incompressible log law. The WMLES prompts transition and peak heating, delays separation, and advances reattachment, thereby shortening the separation bubble. When the shock leads to transition, WMLES provides predictions of DNS peak thermomechanical loads within ±10% at a computational cost lower than DNS by two orders of magnitude. Downstream of the interaction, in the turbulent boundary layer, WMLES agrees well with DNS results for the Reynolds analogy factor, the mean profiles of velocity and temperature, including the temperature peak, and the temperature/velocity correlation.
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In wall-modeled large-eddy simulations (WMLES), the near-wall model plays a significant role in predicting the skin friction, although the majority of the boundary layer is resolved by the outer large-eddy simulation (LES) solver. In this... more
In wall-modeled large-eddy simulations (WMLES), the near-wall model plays a significant role in predicting the skin friction, although the majority of the boundary layer is resolved by the outer large-eddy simulation (LES) solver. In this work, we aim at developing a new ordinary differential equation (ODE)-based wall model, which is as simple as the classical equilibrium model yet capable of capturing non-equilibrium effects and low Reynolds number effects. The proposed model reformulates the classical equilibrium model by introducing a new non-dimensional mixing-length function. The new mixing-length function is parameterized in terms of the boundary layer shape factor instead of the commonly used pressure-gradient parameters. As a result, the newly introduced mixing-length function exhibits great universality within the viscous sublayer, the buffer layer, and the log region (i.e., 0 < y < 0.1δ, where the wall model is typically deployed in a WMLES setup). The performance of the new model is validated by predicting a wide range of canonical flows with the friction Reynolds number between 200 and 5200, and the Clauser pressure-gradient parameter between-0.3 and 4. Compared to the classical equilibrium wall model, remarkable error reduction in terms of the skin friction prediction is obtained by the new model. Moreover, since the new model is ODE-based, it is straightforward to be deployed for predicting flows with complex geometries and therefore promising for a wide range of applications.
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The accurate prediction of aerothermal surface loading is of paramount importance for the design of high speed flight vehicles. In this work, we consider the numerical solution of hypersonic flow over a double-finned geometry,... more
The accurate prediction of aerothermal surface loading is of paramount importance for the design of high speed flight vehicles. In this work, we consider the numerical solution of hypersonic flow over a double-finned geometry, representative of the inlet of an air-breathing flight vehicle, characterized by three-dimensional intersecting shock-wave/turbulent boundary-layer interaction at Mach 8.3. High Reynolds numbers (ReL ≈ 11.6 × 10 6 based on free-stream conditions) and the presence of cold walls (Tw/To ≈ 0.27) leading to large near-wall temperature gradients necessitate the use of wall-modeled large-eddy simulation (WMLES) in order to make calculations computation-ally tractable. The comparison of the WMLES results with experimental measurements shows good agreement in the time-averaged surface heat flux and wall pressure distributions, and the WMLES predictions show reduced errors with respect to the experimental measurements than prior RANS calculations. The favorable comparisons are obtained using an LES wall model based on equilibrium boundary layer approximations despite the presence of numerous non-equilibrium conditions including three dimensionality, shock-boundary layer interactions, and flow separation. Lastly, it is also demonstrated that the use of semi-local eddy viscosity scaling (in lieu of the commonly used van Driest scaling) in the LES wall model is necessary to accurately predict the surface pressure loading and heat fluxes. Nomenclature x,y,z = coordinate in the inertial coordinate system, m L r = reference length for normalization, m t = physical time, s ρ = density, kg/m 3 P = pressure, Pa P 0 = total pressure, Pa T = temperature, K T • = total temperature, K S = constant parameter in the Sutherland's Law, K u = velocity vector, m/s S ij = strain rate tensor, 1/s E = total energy, Pa µ = dynamic viscosity, Pa · s µ t,wm = turbulent eddy viscosity (in wall model), Pa · s k = fluid thermal conductivity, W · m −1 · K −1 c = sound speed, m/s γ = ratio of specific heats Re ∞ = free-stream unit Reynolds number, 1/m Re δ• = Reynolds number based on the boundary layer thickness Q w = wall heat flux, W · m −2 h wm = wall model matching location, m τ w = wall shear stress, Pa u τ = friction velocity at the wall, m/s ν w = wall kinematic viscosity, m 2 /s c p = specific heat capacity at constant pressure, J/K c v = specific heat capacity at constant volume, J/K τ sgs ij = subgrid stress, Pa Q sgs j = subgrid heat flux, W · m −2 α = wedge angle κ = von Kármán constant P r = molecular Prandtl number P r t = turbulent Prandtl number M a = Mach number D = near-wall damping function in the eddy viscosity model y + = dimensionless wall-normal coordinate based on the wall viscous length scale u + = streamwise velocity normalized by the wall friction velocity B = intercept constant in the log law
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In this work, the turbulence statistics in highly supersonic boundary layers downstream of an incident shock wave are investigated by DNS. The objective is to examine the transformations and scaling laws of spatially evolving highly... more
In this work, the turbulence statistics in highly supersonic boundary layers downstream of an incident shock wave are investigated by DNS. The objective is to examine the transformations and scaling laws of spatially evolving highly supersonic boundary layers with a canonical setup. This can allow for the development of efficient reduced-order models for turbulent boundary layers, such as wall-modeled large-eddy simulations (WMLES).
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Unconditionally stable implicit time-marching methods are powerful in solving stiff differential equations efficiently. In this work, a novel framework to handle stiff physical terms implicitly is proposed. Both physical and numerical... more
Unconditionally stable implicit time-marching methods are powerful in solving stiff differential equations efficiently. In this work, a novel framework to handle stiff physical terms implicitly is proposed. Both physical and numerical stiffness originating from convection, diffusion and source terms (typically related to reaction) can be handled by a set of predefined Time-Accurate and highly-Stable Explicit (TASE) operators in a unified framework. The proposed TASE operators act as preconditioners on the stiff terms and can be deployed to any existing explicit time-marching methods straightforwardly. The resulting time integration methods remain the original explicit time-marching schemes, yet with nearly unconditional stability. The TASE operators can be designed to be arbitrarily high-order accurate with Richardson extrapolation such that the accuracy order of original explicit time-marching method is preserved. Theoretical analyses and stability diagrams show that the s-stages sth-order explicit Runge-Kutta (RK) methods are unconditionally stable when preconditioned by the TASE operators with order p ≤ s and p ≤ 2. On the other hand, the sth-order RK methods preconditioned by the TASE operators with order of p ≤ s and p > 2 are nearly unconditionally stable. The only free parameter in TASE operators can be determined a priori based on stability arguments. A set of benchmark problems with strong stiffness is simulated to assess the performance of the TASE method. Numerical results suggest that the proposed framework preserves the high-order accuracy of the explicit time-marching methods with very-large time steps for all the considered cases. As an alternative to established implicit strategies, TASE method is promising for the efficient computation of stiff physical problems.
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In this paper, we extend the method (Fu et al., [1]) to anisotropic meshes by introducing an adaptive SPH (ASPH) concept with ellipsoidal kernels. First, anisotropic target feature-size and density functions, taking into account the... more
In this paper, we extend the method (Fu et al., [1]) to anisotropic meshes by introducing an adaptive SPH (ASPH) concept with ellipsoidal kernels. First, anisotropic target feature-size and density functions, taking into account the effects of singularities, are defined based on the level-set methodology. Second, ASPH is developed such that the particle distribution relaxes towards the target functions. In order to prevent SPH particles from escaping the mesh generation regions, a ghost surface particle method is proposed in combination with a tailored interaction strategy. Necessary adaptations of supporting numerical algorithms, such as fast neighbor search, for enforcing mesh anisotropy are addressed. Finally, unstructured meshes are generated by an anisotropic Delaunay triangulation conforming to the Riemannian met-rics for the resulting particle configuration. The performance of the proposed method is demonstrated by a set of benchmark cases.
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With the observation that the TENO weighting strategy can explicitly distinguish smooth scales from nonsmooth scales in spectral space, in this paper, a new discontinuity indicator is proposed based on the high-order TENO paradigm [Fu et... more
With the observation that the TENO weighting strategy can explicitly distinguish smooth scales from nonsmooth scales in spectral space, in this paper, a new discontinuity indicator is proposed based on the high-order TENO paradigm [Fu et al., JCP 305(2016): 333-359]. The local flow structures are classified as smooth or non-smooth scales, and the hybrid numerical discretization scheme is applied correspondingly , i.e. the high-order upwind linear scheme without characteristic decomposition is employed for resolving smooth scales while the nonlinear low-dissipation TENO scheme is adopted to capture discontinuities. Since the time-consuming characteristic decomposition and smoothness-indicator computation of TENO are avoided in smooth regions, the overall computational efficiency can be improved significantly. Moreover, the cutoff wavenumber separating smooth and nonsmooth scales is determined by the parameter C T. In contrast to the thresholds of other discontinuity indicators , which are typically defined in physical space, C T takes effects in wavespace rendering its high generality. A set of benchmark cases with widespread length-scales is simulated to assess the performance of the proposed discontinuity indicator and the resulting hybrid shock-capturing scheme. Compared to the monotonicity-preserving discontinuity indicator and the TVB discontinuity indicator, the proposed algorithm delivers better performance with a fixed set of parameters for all considered benchmarks .
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In this paper, we propose a new scale-separation formula and develop a very-high-order targeted ENO scheme, which shows exceptional performance in conventional compressible gas dynamics, high-Mach-number simulations with vacuum or... more
In this paper, we propose a new scale-separation formula and develop a very-high-order targeted ENO scheme, which shows exceptional performance in conventional compressible gas dynamics, high-Mach-number simulations with vacuum or near-vacuum region, incompressible and compressible turbulence prediction. The modified TENO weighting strategy can be extended to arbitrarily very-high-order reconstruction in a straightforward manner. The proposed 10-point TENO10-A scheme is optimized to satisfy an approximate-dispersion relation while maintaining the 8th-order accuracy in smooth regions. For conventional gas dynamics at low to moderate Mach numbers, the TENO10-A scheme is robust, and shows low numerical dissipation in resolving small-scale physical fluctuations while capturing the sharp discontinuities. For high-Mach number simulations, TENO10-A is numerically stable and preserves the ENO property with the assistance of a positivity-preserving flux limiter. In terms of turbulent flows, TENO10-A faithfully predicts energy transfer, and resolves vorticity, entropy and acoustic modal fluctuations. A set of benchmark simulations is considered to assess the performance of proposed scheme.
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The recently proposed targeted ENO (TENO) schemes [Fu et al., JCP 305 (2016):333-359] are demonstrated to feature the controllable low numerical dissipation and sharp shock-capturing property in compressible gas dynamic simulations.... more
The recently proposed targeted ENO (TENO) schemes [Fu et al., JCP 305 (2016):333-359] are demonstrated to feature the controllable low numerical dissipation and sharp shock-capturing property in compressible gas dynamic simulations. However, the application of low-dissipation TENO schemes to ideal magnetohydrodynamics (MHD) is not straightforward. The complex interaction between fluid mechanics and electromagnetism induces extra numerical challenges, including simultaneously preserving the ENO-property, maintaining good numerical robustness and low dissipation as well as controlling divergence errors. In this paper, based on an unstaggered constrained transport framework to control the divergence error, we extend a set of high-order low-dissipation TENO schemes ranging from 5-point to 8-point stencils to solving the ideal MHD equations. A unique set of built-in parameters for each TENO scheme is determined. Different from the TENO schemes in [Fu et al., JCP 305 (2016) 333-359], a modified scale-separation formula is developed. The new formula can achieve stronger scale separation, and it is simpler and more efficient than the previous version as the computation cost of high-order global smoothness measure τ K is avoided. The performances of tailored schemes are systematically studied by several benchmark simulations. Numerical experiments demonstrate that the TENO schemes in the constrained transport framework are promising to simulate more complex MHD flows.
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In this paper, we propose an unstructured mesh generation method based on Lagrangian-particle fluid relaxation, imposing a global optimization strategy. With the presumption that the geometry can be described as a zero level set, an... more
In this paper, we propose an unstructured mesh generation method based on Lagrangian-particle fluid relaxation, imposing a global optimization strategy. With the presumption that the geometry can be described as a zero level set, an adaptive isotropic mesh is generated by three steps. First, three characteristic fields based on three modeling equations are computed to define the target mesh-vertex distribution, i.e. target feature-size function and density function. The modeling solutions are computed on a multi-resolution Cartesian background mesh. Second, with a target particle density and a local smoothing-length interpolated from the target field on the background mesh, a set of physically-motivated model equations is developed and solved by an adaptive-smoothing-length Smoothed Particle Hydrodynamics (SPH) method. The relaxed particle distribution conforms well with the target functions while maintaining isotropy and smoothness inherently. Third, a parallel fast Delaunay triangulation method is developed based on the observation that a set of neighboring particles generates a locally valid Voronoi diagram at the interior of the domain. The incompleteness near domain boundaries is handled by enforcing a symmetry boundary condition. A set of two-dimensional test cases shows the feasibility of the method. Numerical results demonstrate that the proposed method produces high-quality globally optimized adaptive isotropic meshes even for high geometric complexity.
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The latest references of high order TENO schemes by Lin Fu
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We develop a parallel fast neighbor search method and communication strategy for particle-based methods with adaptive smoothing-length on distributed-memory computing systems. With a multi-resolution based hierarchical data structure, the... more
We develop a parallel fast neighbor search method and communication strategy for particle-based methods with adaptive smoothing-length on distributed-memory computing systems. With a multi-resolution based hierarchical data structure, the parallel neighbor search method is developed to detect and construct ghost buffer particles, i.e. neighboring particles on remote processor nodes. In order to migrate ghost buffer particles among processor nodes, an undirected graph is established to characterize the sparse data communication relation and is dynamically recomposed. By the introduction of an edge coloring algorithm from graph theory, the complex sparse data exchange can be accomplished within optimized frequency. For each communication substep, only efficient nonblocking point-to-point communication is involved. We consider two demonstration scenarios: (i) fluid dynamics based on smoothed-particle hydrodynamics with adaptive smoothing-length, (ii) a recently proposed physics-motivated partitioning method [Fu et al., JCP 341 (2017): 447-473]. Several new concepts are introduced to recast the partitioning method into a parallel version. A set of numerical experiments is conducted to demonstrate the performance and potential of the proposed parallel algorithms. The proposed methods are simple to implement in large-scale parallel environment and can handle particle simulations with arbitrarily varying smoothing-lengths. The implemented SPH solver has good parallel performance, suggesting the potential for other scientific applications.
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In this paper, we propose an improvement of the five-point and six-point targeted ENO schemes [Fu et al., JCP 305 (2016): 333-359] by introducing an adaptive dissipation control strategy. Nonlinear numerical dissipation is controlled by... more
In this paper, we propose an improvement of the five-point and six-point targeted ENO schemes [Fu et al., JCP 305 (2016): 333-359] by introducing an adaptive dissipation control strategy. Nonlinear numerical dissipation is controlled by dynamically adjusting the cut-off parameter in the TENO weighting strategy according to the first-order smoothness measure of the local flow scales. For the five-point reconstruction, the dissipation bandwidth of the underlying linear scheme is delayed by introducing slight anti-dissipation at low wavenumbers with small dispersion errors. A new sixth order scale-separation parameter τ5 is derived and the modified TENO5-A scheme is third-order accurate. For the six-point reconstruction, dispersion and dissipation error are optimized separately resulting in a modified fourth-order TENO6-A scheme. All necessary parameters are determined by spectral analyses and are shown to be problem-independent by numerical experiments. A set of benchmark cases, including highly compressible gas dynamics, nearly incompressible and compressible turbulence decay, is considered. Numerical experiments demonstrate that both the proposed TENO5-A and TENO6-A scheme show excellent performance for shocks and broadband turbulence. The turbulence statistics obtained with TENO6-A at coarse resolution are comparable to those from the state-of-the-art implicit LES model and agree well with DNS data.
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In Fu et al., (2016), a family of high-order TENO shock-capturing schemes has been proposed for compressible fluid simulations within a finite-difference framework. With the TENO weighting strategy, each candidate stencil is either... more
In Fu et al., (2016), a family of high-order TENO shock-capturing schemes has been proposed for compressible fluid simulations within a finite-difference framework. With the TENO weighting strategy, each candidate stencil is either applied for the final reconstruction with its optimal weight or discarded completely when crossed by discontinuities. In this paper, with the observation that the local flow scales can be judged to be smooth or non-smooth explicitly, we propose a novel low-dissipation finite-volume method based on a new TENO reconstruction. Firstly, a new ENO-like stencil selection paradigm, which adapts between three three-point small stencils and a large candidate stencil, is proposed. The resulting TENO scheme inherits the low-dissipation advantage of original TENO schemes and can be extended to arbitrarily high-order reconstruction without significant complexity increase. The optimal background linear scheme on the three small stencils and that on the large stencil can be optimized either approaching high-order accuracy or better spectral properties separately. Secondly, within the finite-volume framework, a ”low-dissipation” Riemann solver is applied for flux computing when the large candidate stencils for both the left- and right- side reconstruction are judged as smooth whereas a robust ”dissipative” Riemann solver is adopted when one large candidate stencil crosses discontinuities. Since the numerical dissipation from both the reconstruction stage and the flux computing stage can be tuned according to the TENO weighting strategy, the proposed finite-volume method is less-dissipative and provides additional flexibility to handle challenging simulations. A set of benchmark cases is simulated to assess the performance of proposed method.
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In this paper we present a new multi-resolution parallel framework, which is designed for large-scale SPH simulations of fluid dynamics. An adaptive rebalancing criterion and monitoring system is developed to integrate the CVP... more
In this paper we present a new multi-resolution parallel framework, which is designed for large-scale SPH simulations of fluid dynamics. An adaptive rebalancing criterion and monitoring system is developed to integrate the CVP partitioning method as rebalancer to achieve dynamic load balancing of the system. A localized nested hierarchical data structure is developed in cooperation with a tailored parallel fast-neighbor-search algorithm to handle problems with arbitrarily adaptive smoothing-length and to construct ghost buffer particles in remote processors. The concept of “diffused graph” is proposed in this paper to improve the performance of the graph-based communication strategy. By utilizing the hybrid parallel model, the framework is able to exploit the full parallel potential of current state-of-the-art clusters based on Distributed Shared Memory (DSM) architectures. A range of gas dynamics benchmarks are investigated to demonstrate the capability of the framework and its unique characteristics. The performance is assessed in detail through intensive numerical experiments at various scales.
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In [Fu et al., JCP 305(2016): 333-359], a family of high-order targeted ENO (TENO) schemes is proposed. The weighting strategy of TENO either applies a candidate stencil with its optimal weight, or removes its contribution completely when... more
In [Fu et al., JCP 305(2016): 333-359], a family of high-order targeted ENO (TENO) schemes is proposed. The weighting strategy of TENO either applies a candidate stencil with its optimal weight, or removes its contribution completely when it is crossed by discontinuities. This ENO-like stencil selection procedure significantly diminishes the numerical dissipation induced by the nonlinear adaptations of classical WENO schemes. In this paper, the fifth-order TENO scheme is extended to simulate re-active flows in combination with an uncoupled method [1, 2], which splits the reaction source term of detailed chemistry from the flow equations. A set of benchmark cases including the two-dimensional self-sustained detonation is simulated to validate and compare the performance of the fifth-order WENO and TENO schemes. Numerical experiments demonstrate that TENO scheme is robust for simulating chemical reacting flows with using the uncoupled method. In particular, TENO scheme shows better performance in capturing both the shockwaves and the small-scale flow structures, e.g. shear layers and vortices.
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In this paper, we develop an optimal particle setup method for initial condition with Centroidal Voronoi Particle (CVP) dynamics, which combines the Centroidal Voronoi Tessellation (CVT) and Voronoi Particle (VP) concept. CVT optimizes... more
In this paper, we develop an optimal particle setup method for initial condition with Centroidal Voronoi Particle (CVP) dynamics, which combines the Centroidal Voronoi Tessellation (CVT) and Voronoi Particle (VP) concept. CVT optimizes the energy function in terms of compactness and consequently ensures the isotropy of particle distribution. The CVT configuration is computed by Lloyd’s algorithm, which decreases the energy function monotonically. A physics-motivated model equation with tailored equation of state (EOS) is employed to relax the Voronoi particle system such that the convergent equilibrium matches the target configuration. The resulting particle distribution approximates the given analytical profiles of spatially adaptive density, smoothing-length and mass distribution with high interpolation accuracy. The level-set method is introduced to describe arbitrarily complex geometries. A set of Smoothed Particle Hydrodynamics (SPH) simulations is computed to demonstrate the performances of the proposed method. Without parameter tuning, good performance is obtained for presented benchmarks implying its promising potential.
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In [Fu et al., JCP 305(2016): 333-359], a family of high-order targeted ENO (TENO) schemes with a new nonlinear weighting strategy has been proposed. Building upon this strategy, in the current paper, a new class of adaptive TENO schemes... more
In [Fu et al., JCP 305(2016): 333-359], a family of high-order targeted ENO (TENO) schemes with a new nonlinear weighting strategy has been proposed. Building upon this strategy, in the current paper, a new class of adaptive TENO schemes for hyperbolic conservation laws is proposed based on three new concepts: (1) a hierarchical voting strategy is proposed to improve the ENO-like stencil selection; (2) the TENO weighting strategy is extended to function as a built-in discontinuity-location detector. Since the reconstruction scheme must not cross any discontinuity, corresponding target schemes are selected from a set of predefined linear schemes which are optimized towards maximum accuracy order or spectral resolution; (3) based on the observation that the cut-off parameter $C_T$ in the TENO weighting strategy determines nonlinear dissipation, a $C_T$ adaptation strategy is developed to minimize numerical dissipation for high-wavenumber fluctuations while maintaining robustness for shock-capturing. Six-point and eight-point TENO schemes are constructed, and their spectral properties are analyzed by the ADR analysis. A set of benchmark cases is considered to demonstrate the performance of proposed adaptive TENO schemes. Numerical results suggest that the proposed TENO schemes preserve the accuracy order at first and second order critical points and show less numerical dissipation compared with typical WENO schemes. Moreover, the TENO8-NA scheme exhibits good results for both highly compressible flows and nearly incompressible turbulence.
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We propose efficient single-step formulations for reinitialization and extending algorithms, which are critical components of level-set based interface-tracking methods. The level-set field is reinitialized with a single-step (non... more
We propose efficient single-step formulations for reinitialization and extending algorithms, which are critical components of level-set based interface-tracking methods. The level-set field is reinitialized with a single-step (non iterative) "forward tracing" algorithm. A minimum set of cells is defined that describes the interface, and reinitialization employs only data from these cells. Fluid states are extrapolated or extended across the interface by a single-step "backward tracing" algorithm. Both algorithms, which are motivated by analogy to ray-tracing, avoid multiple block-boundary data exchanges that are inevitable for iterative reinitialization and extending approaches within a parallel-computing environment. The single-step algorithms are combined with a multi-resolution conservative sharp-interface method and validated by a wide range of benchmark test cases. We demonstrate that the proposed reinitialization method achieves second-order accuracy in conserving the volume of each phase. The interface location is invariant to reapplication of the single-step reinitialization. Generally, we observe smaller absolute errors than for standard iterative reinitialization on the same grid. The computational efficiency is higher than for the standard and typical high-order iterative reinitialization methods. We observe a 2- to 6- times efficiency improvement over the standard method for serial execution. The proposed single-step extending algorithm, which is commonly employed for assigning data to ghost cells with ghost-fluid or conservative interface interaction methods, shows an about 10-times efficiency improvement over the standard method while maintaining same accuracy. Despite their simplicity, the proposed algorithms offer an efficient and robust alternative to iterative reinitialization and extending methods for level-set based multi-phase simulations.
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The latest references of high-order TENO schemes for conservation laws
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A family of high order TENO (targeted ENO) schemes has been proposed by Fu et al. [JCP 305 (2016): 333-359] [JCP 349 (2017): 97-121]. In this talk, the key concept of TENO schemes and the differences between TENO and WENO will be... more
A family of high order TENO (targeted ENO) schemes has been proposed by Fu et al. [JCP 305 (2016): 333-359] [JCP 349 (2017): 97-121]. In this talk, the key concept of TENO schemes and the differences between TENO and WENO will be addressed, as well as the framework to construct arbitrarily high-order TENO reconstruction. Then, he will introduce the method to optimize and control numerical dispersion and dissipation separately. Thirdly, the TENO schemes capable of capturing shocks and resolving incompressible and compressible turbulence as an implicit LES model will be outlined. At last, he will summarize the wave-resolution property, shock-capturing capability, numerical robustness and the computational efficiency of TENO schemes.
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I dedicate to proposing new high order TENO scheme for Hyperbolic Conservation Laws [ Fu et al. , JCP 305 (2016): 333-359][Fu et al. , JCP 349 (2017): 97-121]. The new schemes are expected to deliver excellent performance for gas... more
I dedicate to proposing new high order TENO scheme for Hyperbolic Conservation Laws [ Fu et al. , JCP 305 (2016): 333-359][Fu et al. , JCP 349 (2017): 97-121]. The new schemes are expected to deliver excellent performance for gas dynamics, incompressible and compressible turbulence. The performances of high order WENO and TENO schemes are intensively investigated. The TENO family schemes are good alternatives to the well-established WENO schemes.
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Although TENO schemes show promising results for turbulence reproduction, they are unsuitable to function as a reliable subgrid LES model by generating excessive dissipation. Meanwhile, the state-of-the-art implicit LES models e.g. the... more
Although TENO schemes show promising results for turbulence reproduction, they are unsuitable to function as a reliable subgrid LES model by generating excessive dissipation. Meanwhile, the state-of-the-art implicit LES models e.g. the localized artificial diffusivity scheme, typically depend on shock sensors, which are case-dependent and fail to retain the monotonicity near discontinuities. The difficulty locates on scale-separating the low-wavenumber smooth regions, high-wavenumber fluctuations and discontinuities sufficiently and incorporating adequate dissipation into numerical schemes correspondingly. In this work, we propose a new 8-point 6th-order TENO8-A scheme. which is motivated for gas dynamics and physics-consistent for incompressible and compress-ible turbulence modeling. While the low-wavenumber smooth region is handled by the optimized linear scheme, with the measurement of local flow scales, the high-wavenumber fluctuations and discontinuities are predicted with adaptive nonlinear dissipation. The new scheme is Galilean invariant and free from physics-based sensors rendering its high generality.
Research Interests:
Why do we need TENO? The development of advanced numerical schemes, that are simultaneously capable of resolving small-scale flow structures and of capturing discontinuities, is a long-standing subject of computational fluid dynamics... more
Why do we need TENO? The development of advanced numerical schemes, that are simultaneously capable of resolving small-scale flow structures and of capturing discontinuities, is a long-standing subject of computational fluid dynamics research. The apparent contradicting requirements of low-dissipation for resolving small-scale flow features and sufficient numerical dissipation for stable capturing of discontinuities pose the key problem. Several approaches , such as total variation diminishing (TVD) schemes, essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) schemes, have been presented in the paper to overcome this problem. While TVD schemes are able to provide sufficient numerical dissipation to capture discontinuities, and to restore formal high-order accuracy in smooth regions without critical points, they degenerate to first-order and produce excessive numerical dissipation near critical points. ENO schemes choose the smoothest stencil to capture discontinuities from a set of candidate approximation stencils and reduce numerical dissipation compared to TVD schemes. WENO schemes exploit a weighted average of approximations from all candidate stencils. Based on the smoothness indicators, the weights are designed to recover the ENO property for capturing discontinuities and to restore the background linear schemes in smooth regions of the solution. WENO schemes are widely used in gas dynamics research. However, for turbulent flow simulations classical WENO schemes exhibit excessive dissipation, which damps the small-scale flow structures significantly. As shown by the approximated dispersion relation (ADR) analysis, the spectral property of WENO schemes is inferior to that of low-dissipation linear schemes. Furthermore, although the classical fifth-order WENO scheme is sufficiently robust for many applications, even higher-order schemes may fail when there exist multiple discontinuities close to each other.
In this thesis, several novel numerical methods, including the high-order shock-capturing targeted Essentially Non-oscillatory (TENO) schemes, smoothed-particle hydrodynamics (SPH) based partitioning method and Centroidal Voronoi Particle... more
In this thesis, several novel numerical methods, including the high-order shock-capturing targeted Essentially Non-oscillatory (TENO) schemes, smoothed-particle hydrodynamics (SPH) based partitioning method and Centroidal Voronoi Particle (CVP) domain decomposition method, are proposed and validated. These methods can be used for high-resolution computational fluid simulations and high-performance scientific computing, which are important to study the physics of fluid dynamics.
Research Interests:
• Poinsot, T. J, and S. K. Lele. "Boundary conditions for direct simulations of compressible viscous flows." Journal of computational physics (1992): 104-129.
Research Interests:
High-order TENO schemes for turbulence (Lin Fu, 傅林)