Interfacial Flows

This paper investigates the use of a shifting algorithm for improving the results of smoothed particle hydrodynamics (SPH) multi-phase simulations by preventing the creation of unnatural voids. Particle shifting occurs according to a Fickian-based algorithm so particles maintain a nearly uniform distribution. A modification of the shifting algorithm is necessary in the air phase to avoid unphysical void formation. In conjunction with the use of graphics processing units (GPUs) for the acceleration of the simulation, the new shifting algorithm allows the simulation of complex multi-phase flows such as a wet dam break and a sloshing tank. Finally, the shifting algorithm is extended to 3-D and validated with the SPHERIC benchmark test case of dam break impacting an obstacle.

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.

A numerical inconsistency has emerged for multi-phase smoothed particle hydrodynamics simulations when using very high resolution, made possible by graphical processing units. In violent flows unphysical voids and phase separation occur ultimately leading to numerical instability. New Fickian-based particle shifting algorithms with a selectively activated free-surface correction are developed for air–water simulations to prevent the creation of unnatural voids and maintain numerical stability through nearly uniform distributions. Using the shifting algorithm without surface correction in the air phase is recommended, with marginal improvements if the shifting algorithm is not applied in water. However, maintaining shifting in water would avoid possible void occurrence. The improvement is demonstrated using a dry-bed dam break and a sloshing tank case. A 3D case involving the impact of the water flow on an obstacle is compared with experimental data. The multi-phase SPH scheme gives ...