A staggered finite volume scheme on general meshes for the Navier-Stokes equations in two space dimensions

Abstract : This paper presents a new finite volume scheme for the incompressible steady-state Navier-Stokes equations on a general 2D mesh. Thescheme is staggered, i.e. the discrete velocities are not located at the same place as the discrete pressures. We prove the existence and the uniqueness of a discrete solution for a centered scheme under a condition on the data, and the unconditional existence of a discrete solution for an upstream weighting scheme. In both cases (nonlinear centered and upstream weighting schemes), we prove the convergence of a penalized version of the scheme to a weak solution of the problem. Numerical experiments show the efficiency of the schemes on vari ous meshes.
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Robert Eymard, Raphaèle Herbin. A staggered finite volume scheme on general meshes for the Navier-Stokes equations in two space dimensions. International Journal on Finite Volumes, Institut de Mathématiques de Marseille, AMU, 2005, 2 (1), pp.1-18. ⟨hal-01112401⟩

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