A nonlinear filter for inviscid fluid flow equations

A nonlinear filter based on artificial dissipation is tested and shown to produce a nonoscillatory shock capturing scheme for hyperbolic systems of conservation laws. In order to control spurious oscillations, the filter is applied after every time step to the solution from a locally implicit scheme for the Euler equation. The method is tested on both unsteady and steady state flow problems in order to demonstrate the efficiency and the efficacy of the technique. On steady state flow problems, an odd/even or red/black ordering of the grid points is considered. This ordering is shown to be robust and also well-suited for implementation on vector computors.