MULTIGRID SOLUTION TO STEADY-STATE 2-DIMENSIONAL CONSERVATION-LAWS

A new genuinely two-dimensional compact approach to discretizing scalar steady-state conservation laws is presented. It provides the possibility to separate treatment of the streamwise and cross-stream directions. Due to this separation, the artificial viscosity can be added in the streamwise direction only. A high-resolution mechanism is introduced in the cross-stream direction. The resulting schemes are shown to be second-order accurate and monotonic, providing a good resolution of discontinuities, representing them in the numerical solution by this oscillation-free transition layers. Due to their good stability properties, the resulting difference equations can be solved efficiently by a multigrid algorithm employing a simple pointwise relaxation. Numerical experiments are presented.