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

We prove in this paper the Lax–Wendroff consistency of a general finite volume convection operator acting on discrete functions which are possibly not piecewise-constant over cells mesh and time steps. It yields an extension theorem for colocated or non-colocated schemes. This result is obtained polygonal polyhedral meshes, under assumptions which, usual practical cases, essentially boil down to flux-consistency constraint; latter is, up our knowledge, novel compares flux at face mean value adjacent cell continuous function applied unknown function. first briefly show how copes with multipoint schemes meshes. then apply it discretisation featuring (convected) scalar variable (convecting) velocity field, staggered approximation, i.e. cell-centred approximation face-centred velocity.