Analysis of first order errors in shock calculations in two space dimensions

摘要

Numerical computations show that solutions of hyperbolic conservation laws obtained by second or higher order shock capturing methods in many cases are only first order accurate downstream of shocks (see, e.g., [M. H. Carpenter and J.H. Casper, AIAA J., 37 (1999), pp. 1072 1079]). We use matched asymptotic expansions to analyze the degeneration in order of accuracy for stationary solutions of hyperbolic conservation laws in two space dimensions.