The convergence of numerical solutions of hydrodynamical shock problems

摘要

Models C and D are mathematical formulations for the motion of materials. Model C is the classical, continuum model, and Model D is an alternative with some advantages. This paper proves a discretization of Model D converges when the material law is the ideal gas with a Navier-Stokes viscosity, the boundary data are given by the zero-velocity boundary conditions, and the initial data are physically acceptable. The discretization is conservative and entropy increasing. This numerical scheme can be used in the calculation of solutions to problems involving shock waves in hydrodynamical materials.