Convergence of a finite volume scheme for the compressible Navier--Stokes system
Provides a rigorous convergence proof for a numerical scheme for the compressible Navier-Stokes equations, which is a fundamental problem in computational fluid dynamics.
The authors prove convergence of a finite volume scheme for the compressible Navier-Stokes system by showing numerical solutions generate a dissipative measure-valued solution, and then use the dissipative measure-valued-strong uniqueness principle to conclude convergence to the strong solution. Numerical experiments support the theory.
We study convergence of a finite volume scheme for the compressible (barotropic) Navier--Stokes system. First we prove the energy stability and consistency of the scheme and show that the numerical solutions generate a dissipative measure-valued solution of the system. Then by the dissipative measure-valued-strong uniqueness principle, we conclude the convergence of the numerical solution to the strong solution as long as the latter exists. Numerical experiments for standard benchmark tests support our theoretical results.