Anomalous physical effects from artificial numerical length scales

Abstract

Shock capturing algorithms are widely used for simulations of compressible fluid flow. Though these algorithms resolve a shock wave within a couple of grid points, the artificial length scale from the numerical shock profile can have side effects. The side effects are similar to physical effects that occur when a relaxation process gives rise to fully or partly dispersed shock waves. Two anomalies due to a non-zero shock width are discussed: (1) in one-dimension, a non-decaying entropy spike results from a transient when a shock profile is formed or changed; (2) in multi-dimensions, front curvature affects the propagation of a shock wave. The authors show that both the entropy anomaly and the curvature effect are a natural consequence of the conservation laws. The same analysis applies both to the continuum equations and to their finite difference approximations in conservation form. Consequently, the artificial length scale inherent in a shock capturing algorithm can mimic real physical effects that are associated with partly dispersed shock waves