CHARACTERISTIC-BASED, ROTATED UPWIND SCHEME FOR THE EULER EQUATIONS

A rotated upwind scheme is developed that calculates shock waves oblique to the grid with nearly the same resolution as shocks that are aligned with the grid. The scheme applies flux difference splitting along two orthogonal directions for each cell face, with the directions computed on the basis of pressure gradient data. Rotated extrapolations and flux limiting are used to generate second-order spatial accuracy. A filtering of the pressure gradient data allows the convergence of the rotated scheme with continuously updated upwinding angles, at a rate comparable to classical schemes. Flux evaluations based on characteristic variables and characteristic boundary conditions are discussed and implemented. The method has been tested on two simple shock reflection problems and formally second-order results capture the oblique shocks with only two to three cells in the shock transition region.