GENUINELY UPWIND ALGORITHMS FOR THE MULTIDIMENSIONAL EULER EQUATIONS

A new method for the solution of the multidimensional Euler equations is presented. As opposed to the classical schemes, it is genuinely multidimensional in that the local characteristic directions, into which information is propagated, are detected. Based on this approach, a conservative cell-centered scheme has been formulated. The numerical fluxes are evaluated using MUSCL extrapolations along the characteristic directions. This leads to a family of first- and second-order accurate schemes with an improved resolution as compared to the classical schemes.