Stability and consistency of a finite difference scheme for compressible viscous isentropic flow in multi-dimension

Motivated by the work of Karper [29], we propose a numerical scheme to compressible Navier- Stokes system in spatial multi-dimension based on finite differences. The backward Euler method is applied for the time discretization, while a staggered grid, with continuity and momentum equations on different grids, is used in space. The existence of a solution to the implicit nonlinear scheme, strictly positivity of the numerical density, stability and consistency of the method for the whole range of physically relevant adiabatic exponents are proved. The theoretical part is complemented by computational results that are performed in two spatial dimensions.