Abstract:This paper revisits the {\em E scheme} of Osher \cite{Osher-SINUM1984} and the {\em flux-limiter scheme} of Sweby for quasi-linear hyperbolic conservation laws \cite{Sweby-SINUM1984}. Part of existing results will be re-understood and some new results will be presented. For a scalar conservation law, except for the conservative monotone schemes, the E scheme is a type of numerical methods that satisfy the discrete entropy condition for any convex entropy, but numerical entropy flux is not unique. Two-point E flux is monotone flux, but multi-point (three or more points) E flux may not necessarily be monotone flux, and multi-point monotone flux may not necessarily be E flux. Sweby's flux-limiter scheme for the quasi-linear conservation laws was built on the E flux-based splitting $f_{j+1}-f_j=f_{j+1} { -\hat{f}^{\text{\tiny E}}_{j+\frac12}+\hat{f}^{\text{\tiny E}}_{j+\frac12}}-f_j$ and the LW scheme. It may not be second-order accurate in both space and time.
From: Huazhong Tang [view email]
[v1]
Tue, 23 Jun 2026 06:12:34 UTC (16 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。