Use of a rotated Riemann solver for the two-dimensional Euler equations (Q1802280)

A scheme for the two-dimensional Euler equations that uses flow parameters to determine the direction for upwind-differencing is described. This approach respects the multi-dimensional nature of the equations and reduces the grid-dependence of conventional schemes. Several angles are tested as the dominant upwinding direction, including the local flow and velocity-magnitude-gradient angles. Roe's approximate Riemann solver is used to calculate fluxes in the upwind direction, as well as for the flux components normal to the upwinding direction.