On the correct numerical shock speed

摘要

When numerical solutions of nonlinear hyperbolic equations are obtained by standard schemes which can handle shocks, extra terms are often added to eliminate post-shock oscillations. If this is not done with care, those extra terms may falsify the shock speed. The question of which type of terms do and do not falsify the shock speed is investigated and it is demonstrated that, when falsification occurs, it can be predicted, both qualitatively and quatitatively.