AN UNSPLIT 3D UPWIND METHOD FOR HYPERBOLIC CONSERVATION-LAWS

An unsplit upwind method for solving hyperbolic conservation laws in three dimensions is developed. This paper derives the algorithm by generalizing a two-dimensional advection algorithm of Van Leer and Colella to three dimensions and then making appropriate modifications. The method is implemented using the equations of gas dynamics. Several test problems are computed to both verify and display the behavior of the method. These test problems include a 1D blast wave, a 2D shock reflection off a 30-degrees ramp, and a 3D astrophysical jet. (C) 1994 Academic Press, Inc.