A numerical method for incompressible and compressible flow problems with smooth solutions

Abstract A semi-implicit difference method of second order in space is introduced for the numerical solution of the Euler equations. If the Mach number e is small, the solutions are second-order accurate also in time. In particular, the solutions converge to an approximate solution of the incompressible equations as e tends to zero. Numerical experiments are presented for channel flow, and the theoretical results (given for the linearized equations) are shown to be valid also for the real nonlinear problem.