A non homogeneous Riemann Solver for shallow water and two phase flows

In this work we consider a two steps finite volume scheme, recently developed to solve nonhomogeneous systems. The first step of the scheme depends on a diffusion control parameter which we modulate, using the limiters theory. Results on Shallow water equations and two phase flows are presented

Schéma SRNHS Analyse et Application d'un schéma aux volumes finis dédié aux systèmes non homogènes

International audienceThis article is devoted to the analysis, and improvement of a finite volume scheme proposed recently for a class of non homogeneous systems. We consider those for which the corressponding Riemann problem admits a selfsimilar solution. Some important examples of such problems are Shallow Water problems with irregular topography and two phase flows. The stability analysis of the considered scheme, in the homogeneous scalar case, leads to a new formulation which has a naturel extension to non homogeneous systems. Comparative numerical experiments for Shallow Water equations with sourec term, and a two phase problem (Ransom faucet) are presented to validate the scheme.Cet article concerne l'analyse et l'application, d'un schéma proposé récemment por une classe de systèmes non homogènes. Nous considérons ceux pour lesquels le problème de Riemann correpondant admet une solution autosimilaire. Deux exemples importants de tels problèmes sont l'écoulement d'eau peu profonde au-dessus d'un fond non plat et les problèmes diphasiques. l'analyse de stabilité du schéma, dans le cas scalaire homogène, amène à une nouvelle écriture qui a une extension naturelle pour le cas non homogène. Des expériences numériques comparatives pour des équations de saint-Venant avec topographie variable, et un problème diphasique (Robinet de Ransom) sont présentés pour évaluer l'efficacité du schéma

Finite volume characteristic flux scheme for transonic flow problems

This work deals with the numerical solution of internal transonic flow problems. Currently we expect 1D and 2D inviscid flow of perfect gas modelled by the Euler equations. We use finite volume characteristic flux scheme, called VFFC scheme, which can be viewed as a generalization of Roe scheme. The dissipation matrix is computed analytically or numerically. We present numerical results for 1D shock tube problem computed by the second order method, where the spatial accuracy is due to linear reconstruction with the minmod limiter and temporal discretization is done using explicit three stage Runge-Kutta method. Further numerical results for 2D transonic flow in GAMM channel have been achieved by the first order method on structured quadrilateral as well as unstructured triangular meshes

A sign matrix based scheme for non-homogeneous PDE's with an analysis of the convergence stagnation phenomenon

International audienceThis work is devoted to the analysis of a finite volume method recently proposed for the numerical computation of a class of non homogenous systems of partial differencial equations of interest in fluid dynamics. The stability analysis of the proposed scheme leads to the introduction of the sign matrix of the flux jacobian. It appears that this formulation is equivalent to the VFRoe scheme introduced in the homogeneous case and has a natural extension here to non homogeneous sys- tems. Comparative numerical experiments for the Shallow Water and Euler equa- tions with source terms, and a model problem of two phase flow (Ransom faucet) are presented to validate the scheme. The numerical results present a convergence stagnation phenomenon for certain forms of the source term, notably when it is singular. Convergence stagnation has been also shown in the past for other numerical schemes. This issue is addressed in a specific section where an explanation is given with the help of a linear model equation, and a cure is demonstrated

Parallel Finite Volume Code for Plasma with Unstructured Adaptive Mesh Refinement

The present paper describes a parallel unstructured-mesh Plasma simulation code based on Finite Volume method. The code dynamically refines and coarses mesh for accurate resolution of the different features regarding the electron density. Our purpose is to examine the performance of a new Parallel Adaptive Mesh Refinement (PAMR) procedure introduced on the ADAPT platform, which resolves of a relatively complicated system coupling the flow partial differential equations to the Poisson's equation. The implementation deals with the MUMPS parallel multi-frontal direct solver and mesh partitioning methods using METIS to improve the performance of the framework. The standard MPI is used to establish communication between processors. Performance analysis of the PAMR procedure shows the efficiency and the potential of the method for the propagation equations of ionization waves

A dynamical adaptive method based on local refinement and unrefinement for triangular finite-element meshes: preliminary results

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Dynamical mesh adaption criteria for accurate capturing of stiff phenomena in combustion

Adaptation criteria for dynamical mesh refinement algorithms aimed for simulating unsteady phenomena are studied in this paper. The applications considered here mainly concern premixed laminar flame propagation in gaseous mixtures, solved by means of a finite-element method in space and explicit time-stepping

Etude numerique de modeles mathematiques decrivant la propagation de flammes dans un milieu gazeux bidimensionnel

CNRS T 63677 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc