Kim Dan Nguyen

Modelling sedimentation–consolidation in the framework of a one-dimensional two-phase flow model

A one-dimensional vertical two-phase flow model for sedimentation–consolidation process is presented. The model is based on solving the continuity and momentum equations for both fluid and solid phases. In the non-cohesive case, the momentum transfer between the two phases is reduced to the drag force around a single particle modified to take the hindrance effects into account. In the cohesive case, Darcy–Gersevanovs law is used for the closure of the momentum transfer between the two phases and the concept of “effective stress” is introduced to take into account the bed structuring. These closure laws are validated against high-resolution experimental data in terms of settling curves and concentration profiles. The reliability of the model is illustrated from an analysis of the momentum balances at different stages during the process. Finally, the proposed closure laws and numerical algorithms are shown to be able to quantitatively reproduce sedimentation of non-cohesive and sedimentation–consolidation of cohesive sediments, including mud.

An improved technique for solving two-dimensional shallow water problems

A numerical model for solving the 2D shallow water equations is proposed herewith. This model is based on a finite volume technique in a generalized co-ordinate system, coupled with a semi-implicit splitting algorithm in which a Helmholtz equation is used for the surface elevation. Several benchmark problems have proven the good accuracy of this method in complex geometries. Nevertheless, several numerical perturbations were noted in the surface elevation. After finding the origin, a new numerical technique is suggested, to avoid these perturbations. Several severe tests are proposed to validate this technique

AN EFFICIENT FINITE DIFFERENCE TECHNIQUE FOR COMPUTING INCOMPRESSIBLE VISCOUS FLOWS

An improved Navier–Stokes solver is presented to compute two-dimensional incompressible flows in the stream–vorticity formulation at high Reynolds number. The technique is based on both the IMM for the non-orthogonal co-ordinate system and a specialized TVD scheme to cope with non-linear transport terms. Numerical results are shown to demonstrate the accuracy and efficiency of the technique. The method is robust and holds promise to handle complex geometries economically.

Parallel SOR methods with a parabolic-diffusion acceleration technique for solving an unstructured-grid Poisson equation on 3D arbitrary geometries

ABSTRACT This paper presents a parallel algorithm for the finite-volume discretisation of the Poisson equation on three-dimensional arbitrary geometries. The proposed method is formulated by using a 2D horizontal block domain decomposition and interprocessor data communication techniques with message passing interface. The horizontal unstructured-grid cells are reordered according to the neighbouring relations and decomposed into blocks using a load-balanced distribution to give all processors an equal amount of elements. In this algorithm, two parallel successive over-relaxation methods are presented: a multi-colour ordering technique for unstructured grids based on distributed memory and a block method using reordering index following similar ideas of the partitioning for structured grids. In all cases, the parallel algorithms are implemented with a combination of an acceleration iterative solver. This solver is based on a parabolic-diffusion equation introduced to obtain faster solutions of the linear systems arising from the discretisation. Numerical results are given to evaluate the performances of the methods showing speedups better than linear.

An Unstructured Finite-Volume Technique for Shallow-Water Flows With Wetting and Drying Fronts

An unstructured finite volume numerical model is presented here for simulating shallow-water flows with wetting and drying fronts. The model is based on the Green’s theorem in combination with Chorin’s projection method. A 2nd -order upwind scheme coupled with a Least Square technique is used to handle convection terms. An Wetting and drying treatment is used in the present model to ensures the total mass conservation. To test it’s capacity and reliability, the present model is used to solve the Parabolic Bowl problem. We compare our numerical solutions with the corresponding analytical and existing standard numerical results. Excellent agreements are found in all the cases.Copyright

Résolution des équations de Saint-Venant par la méthode des volumes finis non structures

Cet article présente une résolution des équations de Saint-Venant par une méthode de projection. Un modèle numérique 2D horizontal est développé par la méthode de volumes finis en maillages non structurés pour calculer des écoulements à surface libre. Deux applications sont aussi présentées dans lesquelles les bathymétries sont complexes. Ce modèle peut être appliqué au calcul des écoulements fluviaux, estuariens et côtiers.