Lax–Wendroff consistency of finite volume schemes for systems of non linear conservation laws: extension to staggered schemes - Archive ouverte HAL Access content directly
Journal Articles SeMa Journal Year : 2022

Lax–Wendroff consistency of finite volume schemes for systems of non linear conservation laws: extension to staggered schemes

Abstract

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 Lax-Wendroff if-theorem for general colocated or non-colocated schemes. This result is obtained for general polygonal or polyhedral meshes, under assumptions which, for usual practical cases, essentially boil down to a flux-consistency constraint; this latter is, up to our knowledge, novel and compares the discrete flux at a face to the mean value over the adjacent cell of the continuous flux function applied to the discrete unknown function. We then apply this result to prove the consistency of a finite volume discretisation of a convection operator featuring a (convected) scalar variable and a (convecting) velocity field, with a staggered approximation, i.e. with a cell-centred approximation of the scalar variable and a face-centred approximation of the velocity.
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Dates and versions

hal-03168277 , version 1 (12-03-2021)
hal-03168277 , version 2 (02-08-2021)

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Cite

T Gallouët, R Herbin, J.-C Latché. Lax–Wendroff consistency of finite volume schemes for systems of non linear conservation laws: extension to staggered schemes. SeMa Journal, 2022, ⟨10.1007/s40324-021-00263-0⟩. ⟨hal-03168277v2⟩
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