题目：Finite Difference MAC Scheme for the Compressible Navier-Stokes Equations
摘要：We propose a new finite difference MAC scheme based on the staggered mesh for the compressible Navier-Stokes equations. The scheme is designed for both Dirichlet and periodic boundary conditions. The key features are the application of upwind flux and artificial diffusion. We show that the scheme is energy stable and convergent to the dissipative measure-valued solution of the system. Using the argument of weak-strong uniqueness [E.Feireisl, P.Gwiazda, A.Swierczewska-Gwiazda, and E.Wiedemann. Dissipative measure-valued solutions to the compressible Navier-Stokes system. Calc.Var.,55–141,2016.], we further conclude that the numerical solution convergences to the strong solution as long as the latter exists on a periodic domain.
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