双同守恒律方程的加权本质无振荡格式新进展

近几年,在计算流体力学中,高精度、高分辨率的加权本质无振荡(weighted essentially non-oscillatory , WENO)格式得到很大的发展.WENO格式的主要思想是通过低阶的数值流通量的凸组合重构得到高阶的逼近,并且在间断附近具有本质无振荡的性质.本文综合介绍了双曲守恒律方程的有限差分和有限体积迎风型WENO,中心WENO,紧致中心WENO以及优化的WENO格式等,讨论了负权的处理和多维问题的解决方法.最后,通过一些算例证明WENO格式的高精度,本质无振荡的性质.图6参40

ADVANCES IN WEIGHTED ESSENTIALLY NON-OSCILLATORY SCHEMES FOR HYPERBOLIC CONSERBATION LAWS

In recent years, high-accurate and high-resolution weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws have been developed in computational fluid dynamics. The basic idea of WENO is to obtain a higher approximation by a linear combination of low order numerical fluxes. In this paper, we will introduce general approaches of finite difference and finite volume upwind WENO, central WENO, compact central WENO and optimize WENO schemes, and discuss strategies of handling negative linear weights and how to solve multi-dimensional problems. In the last part of this paper, we present some numerical examples to demonstrate the accuracy and high-resolution properties of these schemes.