Directionally adapted upwind schemes in 2D for the Euler equations
Abstract
A numerical scheme for the nonlinear Euler equations of gas dynamics in two dimensions is described. It is a generalization of a scheme developed by Roe (1986) for the linearized Euler equations. Onedimensional perturbations can propagate only in two directions, but in two dimensions there are infinitely many directions of propagation. Therefore the algorithm should be able to select the most important directions and to ensure that the scheme uses this information. This paper describes the algorithm and presents some numerical results. It turns out that, for a special test problem in two dimensions, this scheme is more effective concerning the CPU time than dimensional splitting on the basis of the scheme of Harten et al. (1983).
 Publication:

Finite Approximations in Fluid Mechanics II: DFG Priority Research Programme Results 19861988
 Pub Date:
 1989
 Bibcode:
 1989fafm.book..249K
 Keywords:

 Euler Equations Of Motion;
 Gas Dynamics;
 Shock Tubes;
 Shock Waves;
 Two Dimensional Flow;
 Computational Grids;
 Convergence;
 Wind Tunnel Tests;
 Fluid Mechanics and Heat Transfer