A semi-Lagrangian splitting method for the numerical simulation of sediment transport with free surface flows

Alexandre Caboussat, Arwa Mrad, Marco Picasso, Gilles Steiner
PERGAMON-ELSEVIER SCIENCE LTD, 2018
Article

We present a numerical model for the simulation of 3D poly-dispersed sediment transport in a Newtonian flow with free surfaces. The physical model is based on a mixture model for multiphase flows. The Navier-Stokes equations are coupled with the transport and deposition of the particle concentrations, and a volume-of-fluid approach to track the free surface between water and air. The numerical algorithm relies on operator-splitting to decouple advection and diffusion phenomena. Two grids are used, based on unstructured finite elements for diffusion and an appropriate combination of the characteristics method with Godunov's method for advection on a structured grid. The numerical model is validated through numerical experiments. Simulation results are compared with experimental results in various situations for mono-disperse and bi-disperse sediments, and the calibration of the model is performed using, in particular, erosion experiments. (C) 2018 The Authors. Published by Elsevier Ltd.

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Alexandre Caboussat, Arwa Mrad, Marco Picasso, Gilles Steiner
PERGAMON-ELSEVIER SCIENCE LTD, 2018
Article

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https://infoscience.epfl.ch/record/262087?ln=fr

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Numerical simulation of sediment dynamics with free surface flows

Arwa Mrad

We present a numerical model for the simulation of 3D mono-dispersed sediment dynamics in a Newtonian flow with free surfaces. The physical model is a macroscopic model for the transport of sediment based on a sediment concentration with a single momentum balance equation for the mixture (fluid and sediments). The model proposed here couples the Navier-Stokes equations, with a volume-of-fluid (VOF) approach for the tracking of the free surfaces between the liquid and the air, plus a nonlinear advection equation for the sediments (for the transport, deposition, and resuspension of sediments). The numerical algorithm relies on a splitting approach to decouple diffusion and advection phenomena such that we are left with a Stokes operator, an advection operator, and deposition/resuspension operators. For the space discretization, a two-grid method couples a finite element discretization for the resolution of the Stokes problem, and a finer structured grid of small cells for the discretization of the advection operator and the sediment deposition/resuspension operator. SLIC, redistribution, and decompression algorithms are used for post-processing to limit numerical diffusion and correct the numerical compression of the volume fraction of liquid. The numerical model is validated through numerical experiments. We validate and benchmark the model with deposition effects only for some specific experiments, in particular erosion experiments. Then, we validate and benchmark the model in which we introduce resuspension effects. After that, we discuss the limitations of the underlying physical models. Finally, we consider a one-dimensional diffusion-convection equation and study an error indicator for the design of adaptive algorithms. First, we consider a finite element backward scheme, and then, a splitting scheme that separates the diffusion and the convection parts of the equation.

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A numerical model is presented for the simulation of complex fluid flows with free surfaces. The unknowns are the velocity and pressure fields in the liquid region, together with a function defining the volume fraction of liquid. Although the mathematical formulation of the model is similar to the volume of fluid (VOF) method, the numerical schemes used to solve the problem are different. A splitting method is used for the time discretization. At each time step, two advection problems and a generalized Stokes problem are to be solved. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small rectangular cells, using a forward characteristic method. The generalized Stokes problem is solved using a finite element method on a fixed, unstructured mesh. Numerical results are presented for several test cases: the filling of an S-shaped channel, the filling of a disk with core, the broken dam in a confined domain. (C) 1999 Academic Press.

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Numerical simulation of three-dimensional free surface flows

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A numerical model is presented for the simulation of complex fluid flows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2):439) is extended to three dimensional situations. The mathematical formulation of the model is similar to that of the volume of fluid (VOF) method, but the numerical procedures are different. A splitting method is used for the time discretization. At each time step, two advection problems-one for the predicted velocity field and the other for the volume fraction of liquid-are to be solved. Then, a generalized Stokes problem is solved and the velocity field is corrected. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small cubic cells, using a forward characteristic method. The generalized Stokes problem is solved using continuous, piecewise linear stabilized finite elements on a fixed, unstructured mesh of tetrahedrons. The three-dimensional implementation is discussed. Efficient postprocessing algorithms enhance the quality of the numerical solution. A hierarchical data structure reduces memory requirements. Numerical results are presented for complex geometries arising in mold filling. Copyright (C) 2003 John Wiley Sons, Ltd.

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