227 citations · 323 across the 28 of their papers we have counts for
33 papers
Optimal error estimates for non-conforming approximations of linear parabolic problems with minimal regularity
J Droniou, R Eymard, T Gallouët +2
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler…
A MUSCL-like finite volumes approximation of the momentum convection operator for low-order nonconforming face-centred discretizations
Aubin Brunel, Raphaele Herbin, Jean-Claude Latché
We propose in this paper a discretization of the momentum convection operator for fluid flow simulations on quadrangular or hexahedral meshes. The space discretization is performed…
A staggered scheme for the compressible Euler equations on general 3D meshes
Aubin Brunel, Raphaèle Herbin, Jean-Claude Latché
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 hexah…
Convergence of the fully discrete incremental projection scheme for incompressible flows
Thierry Gallouët, Raphaèle Herbin, Jean-Claude Latché +1
The present paper addresses the convergence of a first order in time incremental projection scheme for the time-dependent incompressible Navier-Stokes equations to a weak solution,…
A Consistent Quasi-Second Order Staggered Scheme for the Two-Dimensional Shallow Water Equations
R Herbin, J. -C Latché, Y Nasseri +1
A quasi-second order scheme is developed to obtain approximate solutions of the shallow water equationswith bathymetry. The scheme is based on a staggered finite volume scheme for…
Convergence of the implicit MAC-discretized Navier--Stokes equations with variable density and viscosity on non-uniform grids
Léa Batteux, Thierry Gallouët, Raphaele Herbin +2
The present paper is focused on the proof of the convergence of the discrete implicit Marker-and-Cell (MAC) scheme for time-dependent Navier--Stokes equations with variable density…
Finite volume schemes and Lax-Wendroff consistency
R Eymard, T Gallouët, R Herbin +1
We present a (partial) historical summary of the mathematical analysis of finite differences and finite volumes methods, paying a special attention to the Lax-Richtmyer and Lax-Wen…
Weak Consistency of Finite Volume Schemes for Systems of Non Linear Conservation Laws: Extension to Staggered Schemes
T Gallouët, R Herbin, J. -C Latché
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…
Modelling of a spherical deflagration at constant speed
D Grapsas, R Herbin, J. -C Latché +1
We build in this paper a numerical solution procedure to compute the flow induced by a spherical flame expanding from a point source at a constant expansion velocity, with an insta…
A staggered pressure correction numerical scheme to compute a travelling reactive interface in a partially premixed mixture
D Grapsas, Raphaèle Herbin, J. -C Latché +1
We address in this paper a model for the simulation of turbulent deflagrations in industrial applications. The flow is governed by the Euler equations for a variable composition mi…
Non-conforming finite elements on polytopal meshes
Jerome Droniou, Robert Eymard, Thierry Gallouet +1
In this work we present a generic framework for non-conforming finite elements on polytopal meshes, characterised by elements that can be generic polygons/polyhedra. We first prese…
A Class of Collocated Finite Volume Schemes for Incompressible Flow Problems
R. Eymard, R. Herbin, J. -C Latché +1
In this paper, we present a class of finite volume schemes for incompressible flow problems. The unknowns are collocated at the center of the control volumes, and the stability of…
Conservativity and Weak Consistency of a Class of Staggered Finite Volume Methods for the Euler Equations
R. Herbin, J. -C. Latché, S. Minjeaud +1
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 materi…
Consistent Internal Energy Based Schemes for the Compressible Euler Equations
R. Herbin, T. Gallouët, J. -C Latché +1
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to e…
A decoupled staggered scheme for the shallow water equations
Raphaèle Herbin, Jean-Claude Latché, Youssouf Nasseri +1
We present a first order scheme based on a staggered grid for the shallow water equations with topography in two space dimensions, which enjoys several properties: positivity of th…
On The Weak Consistency of Finite Volumes Schemes for Conservation Laws on General Meshes
Thierry Gallouët, R. Herbin, J. -C Latché
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 bala…
The gradient discretisation method for linear advection problems
Jérôme Droniou, Robert Eymard, T. Gallouët +1
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equation…
A unified analysis of elliptic problems with various boundary conditions and their approximation
Jérôme Droniou, Robert Eymard, T. Gallouët +1
We design an abstract setting for the approximation in Banach spaces of operators acting in duality. A typical example are the gradient and divergence operators in Lebesgue--Sobole…
Low Mach number limit of some staggered schemes for compressible barotropic flows
R. Herbin, J. -C Latché, Khaled Saleh
In this paper, we study the behaviour at low Mach number of numerical schemes based on staggered discretizations for the barotropic Navier-Stokes equations. Three time discretizati…
Entropy estimates for a class of schemes for the euler equations
Thierry Gallouet, Raphaele Herbin, J. -C Latché +1
In this paper, we derive entropy estimates for a class of schemes for the Euler equations which present the following features: they are based on the internal energy equation (even…
Convergence of the mac scheme for variable density flows
Thierry Gallouët, Raphaele Herbin, Jean-Claude Latché +1
We prove in this paper the convergence of an semi-implicit MAC scheme for the time-dependent variable density Navier-Stokes equations.
Two models for the computation of laminar flames in dust clouds
Dionysios Grapsas, Raphaele Herbin, J Latché
We address two models for the simulation of dust clouds premixed combustion: the first one consists in usual balance equations, to derive the second one, we suppose that the soluti…
Analysis of a fractional-step scheme for the P1 radiative diffusion model
Raphaele Herbin, Thierry Gallouët, Jean-Claude Latché +1
We address in this paper a nonlinear parabolic system, which is built to retain the main mathematical difficulties of the P1 radiative diffusion physical model. We propose a finite…
Low Mach number limit of a pressure correction MAC scheme for compressible barotropic flows
Raphaele Herbin, J. -C. Latché, K. Saleh
We study the incompressible limit of a pressure correction MAC scheme [3] for the unstationary compressible barotropic Navier-Stokes equations. Provided the initial data are well-p…