Finite Difference Scheme for Barotropic Gas Equations

An implicit finite difference scheme approximating the equations of barotropic gas flow is proposed. This scheme ensures the positivity of density and the validity of an energy inequality and the mass conservation law. The continuity equation is approximated implicitly. It is proved that the resulting system of nonlinear equations has a solution for any time and space stepsizes. An iterative method for solving the system of nonlinear equations at each time step is proposed.