Related papers: Finite volume schemes and Lax-Wendroff consistency
We prove in this paper the weak consistency of a general finite volume convection operator acting on discrete functions which are possibly not piecewise-constant over the cells of the mesh and over the time steps. It yields an extension of…
The aim of this paper is to develop some tools in order to obtain the weak consistency of (in other words, analogues of the Lax-Wendroff theorem for) finite volume schemes for balance laws in the multi-dimensional case and under minimal…
Since early publications in the late 1980s and early 1990s, the finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of the method, which can be classified in a variety of ways,…
We are interested in the large-time behavior of solutions to finite volume discretizations of convection-diffusion equations or systems endowed with non-homogeneous Dirichlet and Neumann type boundary conditions. Our results concern various…
We address a class of schemes for the Euler equations with the following features: the space discretization is staggered, possible upwinding is performed with respect to the material velocity only and the internal energy balance is solved,…
We propose a finite volume scheme for convection-diffusion equations with nonlinear diffusion. Such equations arise in numerous physical contexts. We will particularly focus on the drift-diffusion system for semiconductors and the porous…
The aim of this work is to propose a provably convergent finite volume scheme for the so-called Stefan-Maxwell model, which describes the evolution of the composition of a multi-component mixture and reads as a cross-diffusion system. The…
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on a monolithic convex limiting approach and prove a…
This paper is focused on the approximation of the Euler equations of compressible fluid dynamics on a staggered mesh. With this aim, the flow parameters are described by the velocity, the density and the internal energy. The thermodynamic…
A framework of finite-velocity model based Boltzmann equation has been developed for convection-diffusion equations. These velocities are kept flexible and adjusted to control numerical diffusion. A flux difference splitting based kinetic…
We address here the discretization of the momentum convection operator for fluid flow simulations on 2D triangular and quadrangular meshes and 3D polyhedral meshes containing hexahedra, tetrahedra, prisms and pyramids. The finite volume…
We study the water hammer problem in the case of a sudden closing of a valve upstream, and we consider a Lax-Wendroff finite difference scheme in order to obtain a numerical solution of this problem. In order to establish the approximation…
We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection…
In this paper, we propose a novel development in the context of entropy stable finite-volume/finite-difference schemes. In the first part, we focus on the construction of high-order entropy conservative fluxes. Already in [LMR2002], the…
This paper presents stability and convergence analysis of a finite volume scheme (FVS) for solving aggregation, breakage and the combined processes by showing Lipschitz continuity of the numerical fluxes. It is shown that the FVS is second…
We study convergence of a finite volume scheme for the Navier-Stokes-Fourier system describing the motion of compressible viscous and heat conducting fluids. The numerical flux uses upwinding with an additional numerical diffusion of order…
We present a stochastic and variational aspect of the Lax-Friedrichs scheme applied to hyperbolic scalar conservation laws. This is a finite difference version of Fleming's results ('69) that the vanishing viscosity method is characterized…
We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy functionals. For this kind of models including porous media…
A new framework is proposed for analyzing staggered-grid finite difference finite volume methods on unstructured meshes. The new framework employs the concept of external approximation of function spaces, and gauge convergence of numerical…
A new finite volume (FV) discretisation method for the Lattice Boltzmann (LB) equation which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic…