Jonathan Lambrechts

An unstructured-mesh, finite element, depth-integrated model of the hydrodynamics of the whole Great Barrier Barrier Reef (GBR), Australia, has been developed and implemented on a parallel computer. Far away from reefs, islands and important bathymetric features, the mesh size may be as large as a few kilometres, whereas, in the vicinity of reefs and islands, the grid is drastically refined, leading to meshes that can be 100 metres in size. This enables our model to simulate motions characterized by a wide range of space and time scales. Large scale currents, i.e. the tides, the wind-induced circulation and the bifurcation of the East Australian Current, are reproduced with an accuracy that is comparable to that achieved by today’s largescale models of the GBR. The model is also successful at representing small-scale processes, such as tidal jets, their instabilities, as well as the eddies developing in the wake of islands and headlands. The influence of the small scales on the large scales has been investigated. The model will be used for studying the connectivity between subdomains of the GBR. Once validated, an ecological module will be coupled with the present hydrodynamic code.

The development of suitable and fast time integration methods for ocean modeling con- stitutes an important challenge. No single time-discretisation works well for all physical processes in a complex marine model, as dierent subsystems have widely dierent charac- teristics in terms of time scales, dynamic behaviour, and accuracy requirements. We believe that building appropriate time stepping strategies for multi-scale computations will enable us to gain an order of magnitude. Indeed, unstructured-mesh generation processes are complex and, even though it is possible to control average element sizes in specic regions of the domain, it is not the case for each element size. The smallest element is usually much more smaller than the criterion that was prescribed a priori and it determines the stable time step for the entire model. Therefore, the computational eciency of explicit time-stepping methods may be drastically low. Multirate schemes represent a class of methods that use variou...

Gmsh is an open-source three-dimensional finite element grid generator with a build-in CAD engine and post-processor. Its design goal is to provide a fast, light and user- friendly meshing tool with parametric input and advanced visualization capabilities. This paper presents new developments that are available in GMSH in different topics of mesh generation. We will focus mainly on curvilinear meshing, surface reparametrization and quad/hex meshing.

The development of suitable and fast time integration methods for ocean modeling constitutes an important challenge. No single time-discretisation works well for all physical processes in a complex marine model, as different subsystems have widely different characteristics in terms of time scales, dynamic behaviour, and accuracy requirements. The primitive equations for ocean flows allow for the existence of phenomena exhibiting a wide spectrum of propagation speeds. Typically, external gravity waves propagate at 101 − 102 ms−1 and internal waves at a few meters per second, whereas advection is characterized by speeds ranging from 10−3 to 1 ms−1. We believe that building appropriate time stepping strategies for multi-scale computations will enable us to gain an order of magnitude. For instance, consider the case of a typical mesh of the Great Barrier Reef (GBR) made up of about 1 million triangles. Element sizes were determined in order to capture the relevant bathymetric and topogr...

The hydrosphere is made up of a number media, such as the oceans, the shelf seas, the estuaries, the rivers, the land surface and ground water as well as the sea ice - which, for the sake of simplicity, is considered herein to be part of the hydrosphere. The processes taking place in these domains are vastly different in nature and are characterized by a wide range of space- and time-scales. The components of the hydrosphere interact with each other. For instance, the shallow marine and estuarine regions, though accounting for less than 1% of the volume of the oceans, have a biomass far from negligible as compared to that of the oceans, implying that they play a significant role in global biogeochemical cycles. This is one of the reasons why models are now needed that deal with most, if not all, of the components of the hydrospheric system. Numerical models of each of the components of the hydrosphere already exist. However, an integrated model of the whole hydrosphere has yet to be...

We present a model to solve grains/ uid ows. Mixtures of grains and uids occur in a large number of industrial and geophysical applications like uidised beds, mixing, mud ows, landslides, submarine avalanches, etc. The granular phase is solved by a contact dynamics method at the particle scales. For the hydrodynamic part, we solve the incompressible Navier-Stokes-Brinkman equations in a porous media by a nite element method. Those equations represent in a single model a continuous transition between the Darcy regime at high particle concentration and a classical Navier-Stokes ow at low concentration. At high Reynolds number, the term of Forchheimer is used to take the particle shapes into account. This approach allows the simulation of a granular phase with a large number of particles with dierent size, shape, and compactness. The interactions between the grains and the uid mixture occurs at a mesoscopic scale. The mesoscopic scale is chosen independently of the mesh resolution of t...

In the recent years, high-order numerical methods have been shown to yield superior computational efficiency in problems with high resolution requirements, compared to standard second-order solvers based on Finite Volume technology. However, as the maturity of high-order schemes such as Discontinuous Galerkin methods is being brought to the level of practical application, many contributions show that their accuracy strongly depends on the accuracy of the geometrical discretization (see for instance [1]). It is thus necessary to develop the matching curvilinear mesh generation technology in order to fully benefit from the efficiency of high-order schemes. In this talk, we will present the methods that have been developed in the framework of the IDIHOM project for the generation of high-order unstructured meshes. We adopt an indirect approach that consists in creating first a linear unstructured (or hybrid mesh), and then curving its boundaries to match the geometry. This often result...

The Tonle Sap Lake, which is located in the Cambodian floodplain of the Mekong River System, plays an important role for storage and water supply in Cambodia as well as in the low land region of the Mekong River System. Every year the lake stores water in the flood season from May to October while it acts as a spillway providing water to the Mekong Delta in the dry season from November to April. In other words, the lake depth can rise by approximately 10 m and the water volume can increase 5 times during the year, showing various drying and wetting areas in the lake and its adjacent floodplains. In terms of hydrodynamic modelling, these wetting/drying areas are still challenging because of several difficulties, e.g. large CPU time, slow transition of wet-dry interface and, possibly lack of mass conservation. In this paper, we present a wetting drying algorithm with a limitation for the fluid depth and a blending parameter in order to ensure local mass conservation and rapid transiti...

An unstructured-mesh, finite element, depth-integrated model o f the hydrodynamics o f the whole G reat Barrier Barrier Reef (GBR), Australia, has been developed and implemented on a parallel computer. Far away from reefs, islands and im portant bathymetric features, the mesh size may be as large as a few kilometres, whereas, in the vicinity o f reefs and islands, the grid is drastically refined, leading to meshes that can be 100 metres in size. This enables our model to simulate motions characterized by a wide range o f space and time scales. Large scale currents, i.e. the tides, the w ind-induced circulation and the bifurcation o f the East Australian Current, are reproduced with an accuracy that is com parable to that achieved by today's large-scale models o f the GBR. The model is also successful at representing small-scale processes, such as tidal jets, the ir instabilities, as well as the eddies developing in the wake o f islands and headlands. Both large and small scales ...

While a consensus is forming in the computational physics community on the superior efficiency of high-order numerical schemes, it has been shown that linear geometrical discretizations can deprive such schemes from their benefits. The need for curvilinear mesh generation tools is becoming more acute as high-order methods are being brought to the level of practical applications. In this talk, we report on the development of a high-order unstructured mesh generation method based on an unconstrained optimization procedure [1], occasionally supplemented with an analytical technique. As invalid elements often appear when creating high-order meshes, emphasis is put on robustness: the optimization procedure is specifically designed to enforce mesh validity, that is evaluated through the estimation of provably correct bounds for the Jacobian of the elements [2]. The objective function can also account for the distance between the real geometry and the mesh boundary, in order to optimize th...

Suspended particulate matter has a great influence on most of the biological and chemical organisms in aquatic environments. A good representation of the sediment dynamics is therefore essential for ecological modeling. To this purpose, a fine sediment module is developed and coupled to the two-dimensional component of the finite-element model SLIM. In this module, two tracers are calculated: the concentration of suspended sediments and the concentration of sediments on the bottom. The first one is transported according to the hydrodynamics and diffused, while the second one does not move. Classical parameterizations of erosion and deposition allow exchange between tracers. The talk focusses on two studies using SLIM and implying sediments. The first case studied is the Scheldt Estuary (Belgium, the Netherlands). The model, covering the whole continental shelf, the estuary, the tidal river and the main tributaries of the Scheldt, is thoroughly multi-scale (de Brye et al, 2010). In t...

An unstructured-mesh parallel hydrodynamical model of the whole Great Barrier Reef is presented. The depth-averaged equations of motion are discretized in space by means of a mixed finite element formulation while the time marching procedure is based on a third order explicit Adams-Bashforth scheme. The mesh is made up of triangles. The size and the shape of the triangles can be modified easily so as to resolve a wide range of scales of motion, from those of the regional flows to those of the eddies or tidal jets that develop in the vicinity of reefs and islands. The forcings are the surface wind stress, the tides and the East Australian Current, the latter two forcings being applied along the open boundaries of the computational domain. The numerical results compare favourably with observations of both alongshores currents due to the East Australian Current and the local pertubations due to narrow reef passages. Comparisons are also performed with the simulations of a three-dimensi...

Abstract This paper is devoted to the investigation of the density sorting of grains using water jigging. Experiments achieved in a laboratory scale water jig for two initial binary bed configurations are studied and compared to numerical results. The vertical composition of the deposit is estimated after different number of water pulses to represent the sorting evolution in time. Simulations are based on a multiscale model in which the fluid is solved at a larger scale than the grain diameter using the finite element method, while the grains are considered as rigid bodies and solved using the nonsmooth contact dynamics. Key parameters are numerically varied and observed to determine the sensitivity of the process.

A 3D frame consists of three mutual orthogonal (unit) vectors, defining a local basis. There mainly exist three ways to represent 3D frames: combination of rotations, spherical harmonics and fourth order tensor. We propose here a representation carried out by the special unitary group. The article strongly relies on Du Val (1964). We first describe the rotations with quaternions, Du Val (1964) §3-15. We define and show the isomorphism between unit quaternions and the special unitary group, Du Val (1964) §16. The frame field space is identified as the quotient group of rotations by the octahedral group, Du Val §20. The invariant forms of the vierer, tetrahedral and octahedral groups are successively built, without using homographies Du Val §39. Modifying the definition of the isomorphism between unit quaternions and the special unitary group allows to use the invariant forms of the octahedral group as a unique parameterization of the orientation of 3D frames. The parameterization con...

. Lake Tanganyika is the second oldest (oldest basin of the lake is 9–12 million years old), second deepest (1470 m) lake in the world. It holds 16 % of the world's liquid freshwater. Approximately 100 000 people are directly involved in the fisheries operating from almost 800 sites along its shores. Despite the vital importance of Lake Tanganyika and other African inland waters for local communities, very little is known about the impacts of future climate change on the functioning of these lacustrine systems. This is remarkable, as projected future changes in climate and associated weather conditions are likely to influence the hydrodynamics of African water bodies, with impacts cascading into ecosystem functioning, fish availability and water quality. Here we project the future changes in the hydrodynamics of Lake Tanganyika under a high-end emission scenario using the 3D version of the Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM 3D) forced by a highresolution regional climate model. We first show the added value of 3D simulations compared to previously obtained 1D model results. The simulated interseasonal variability of the lake with this 3D model explains how the current mixing system works. A short-term present-day simulation (10 years) shows that the 75 m deep thermocline moves upward in the south of the lake until the lower layer reaches the lake surface during August and September. Two 30-year simulations have been performed (one with present day and one with future conditions), such that a comparison can be made between the current situation and the situation at the end of the 21st century. The results show that the surface water temperature increases on average by 3 ± 0.5 K. The latter influences the hydrodynamics in the top 150 m of the lake, namely the bottom of the thermocline does not longer surface. This temperature-induced stratification fully shuts down the earlier explained mixing mechanism.

Age can be evaluated at any time and position to understand transport processes taking place in the aquatic environment, including for reactive tracers. In the framework of the Constituent-oriented Age and Residence time Theory (CART), the age of a constituent or an aggregate of constituents, including the water itself, is usually defined as the time elapsed since leaving the boundary where the age is set or reset to zero. The age is evaluated as the ratio of the age concentration to the concentration, which are the solution of partial differential equations. The boundary conditions for the concentration and age concentration cannot be prescribed independently of each other. Instead, they must be derived from boundary conditions designed beforehand for the age distribution function (the histogram of the ages, the age theory core variable), even when this variable is not calculated explicitly. Consistent boundary conditions are established for insulating, departure and arrival bounda...

<p>The Congo River region of freshwater influence (ROFI) is characterized by a deep canyon that connects the river to the deep ocean by cutting through the continental shelf (Shepard & Emery, 1973). In the estuary, high discharge of freshwater and very small vertical mixing within the canyon restricts the supply of oxygen from the surface waters to the more saline bottom waters, where the remineralisation of riverine particulate organic carbon leads to hypoxia (Eisma & Van Bennekom, 1978). We study the dynamics of the Congo River ROFI by applying the multi-scale baroclinic coastal ocean model SLIM 3D (www.slim-ocean.be) to this challenging environment. Model results compare favourably against in-situ observation in the estuary, suggesting that the exchange flow is correctly simulated. Using water ages as a diagnostic tool allows gaining deeper insight into the fate of riverine and oceanic water.</p><p>We use the simulated renewing time of the canyon’s water body by oceanic water (R = 20 d) to calculate an oxygen and carbon budget of the subhalocline water body from the remineralization of POC.</p><p>The renewing oceanic waters originate from the Eastern Atlantic equatorial oxygen minimum zone.  At a representative station in the canyon 60 km offshore the oxygen concentration was measured as 0,05 – 0,1 [mol O<sub>2</sub>/m3] at water depths of 200 - 500 [m]. Following Eisma & Kalf (1984) we split the recent Congo River POC flux of 5260 [mol C s<sup>-1</sup>] (Coynel et al., 2005) into 50 % settling into the subhalocline water body, the other 50 % being advected offshore with the surface plume. Given these assumptions for the oxygen and carbon boundary fluxes, only 15 % of the settling POC are remineralised by aerobic degradation within the canyon, confirming oxygen limitation and leaving a substantial fraction of available labile POC undegraded (generally 35 % of tropical riverine POC are labile; Ittekkot, 1988). Summing up, the canyon’s oxygen balance is ocean oxygen- rather than river POC - controlled, and scenarios of even substantial future POC-flux reductions by land use change and/or reservoir construction within the catchment should therefore not imply significant changes in the Congo River estuarie’s oxygen balance.</p><p>Coynel, A., P. Seyler, H. Etcheber, M. Meybeck  &  D. Orange (2005) Spatial and seasonal dynamics of total and suspended sediment and organic carbon species in the Congo River. Global Biogeochemical Cycles, <strong>19</strong>,GB4019, doi: 10.1029/2004GB002335.</p><p>Eisma, D. & A.J. Van Bennekom (1978) The Zaire river and estuary and the Zaire outflow in the Atlantic Ocean. Netherlands J. Sea Res. <strong>12</strong> (3-4): 255-272.</p><p>Eisma, D. & J. Kalf (1984) Dispersal of…