An Implementation of a Grid-Independent Upwind Scheme for the Euler Equations

A scheme for the twedimensional Euler equations that uses flow parameters to determine the direction for upwind-differencing is described. This approach reduces the grid-dependence of conventional schemes. Upwinding at the local flow angle and the local pressure-gradient angle is tested. The upwindbiased fluxes are calculated with Roe's approximate Riemann solver. A centered flux is used for the component normal t o the upwinding direction. Results for a first-order scheme show significant improvement over conventional grid-aligned upwinding. Specifically, oblique shock waves are less diffused. Preliminary results for a second-order scheme are also included.