A Two-step Godunov-type Scheme for the Euler Equations

A second-order Godunov-type scheme for the Euler equations in conservation form is derived. The method is based on the EN0 formuation proposed by Harten et aI. The fundamental difference lies in the use of a two-step scheme to compute the time evolution. The scheme is TVD in the linear scalar case, and gives oscillation-free solutions when dealing with nonlinear hyperbolic systems. The admissible time step is twice that of classical Godunov- type schemes. This feature makes it computationally cheaper than one-step schemes, while requiring the same computer storage.