An Evaluation of Several Differencing Methods for Inviscid Fluid Flow Problems

Abstract An evaluation was made of five algorithms for ideal inviscid flow: Lax's, Rusanov's, Landshoff's, the Lax-Wendroff, and Richtmyer's. These algorithms were compared on the basis of ease of coding, spatial and temporal resolution, and execution time. The comparisons were drawn through studies of a one-dimensional reflected shock wave, a flat-faced step in supersonic flow, and passage of a normal shock wave over a stationary cone. Lax's method was found to be the easiest to implement and of good resolution; Rusanov's to be the most versatile and of better resolution; and a modified version of the Lax-Wendroff to yield the best resolution but to be the most difficult and time-consuming to use.