Convergence of the MAC scheme for the incompressible Navier-Stokes equations

Abstract

We prove in this paper the convergence of the Marker and cell (MAC) scheme for the dis-cretization of the steady-state and unsteady-state incompressible Navier-Stokes equations in primitive variables on non-uniform Cartesian grids, without any regularity assumption on the solution. A priori estimates on solutions to the scheme are proven ; they yield the existence of discrete solutions and the compactness of sequences of solutions obtained with family of meshes the space step of which tends to zero. We then establish that the limit is a weak solution to the continuous problem.

accepté pour publication dans Foundations of Computational Mathematics

Cited by in corpus (8)

• Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods
• Convergence of the fully discrete incremental projection scheme for incompressible flows
• A decoupled staggered scheme for the shallow water equations
• On convergence of Chorin's projection method to a Leray-Hopf weak solution
• Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations
• Convergence of the implicit MAC-discretized Navier--Stokes equations with variable density and viscosity on non-uniform grids
• Low Mach number limit of a pressure correction MAC scheme for compressible barotropic flows
• A Consistent Quasi-Second Order Staggered Scheme for the Two-Dimensional Shallow Water Equations