An improved accurate monotonicity-preserving scheme for the Euler equations
An improved accurate monotonicity-preserving scheme for the Euler equations
复制标题
欧拉方程的一种改进的精确单调性保持格式
DOI：
10.1016/j.compfluid.2016.09.002
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发表时间：
2016
影响因子：
2.8
通讯作者：
Tian Baolin
中科院分区：
文献类型：
--
作者：
He Zhiwei;Zhang Yousheng;Gao Fujie;Li Xinliang;Tian Baolin
Suresh 和 Huynh (1997) [5] 的准确单调性保持 (MP) 方案是双曲守恒定律的高阶、高分辨率方法。然而，MP方案的鲁棒性不是很高。本文对该方案进行了详细分析，揭示了鲁棒性较弱的两个潜在原因。此外，为了增强MP格式的鲁棒性，提出了MP格式的改进版本，其中在受干扰的不连续点处使用严格的连续总变差递减(TVD)数值通量，使得振荡不会在不违反TVD条件的情况下无限增长。在不破坏超高分辨率特性的情况下，数值试验表明改进方案在模拟极端数值试验方面具有很强的鲁棒性。
The accurate monotonicity-preserving (MP) scheme of Suresh and Huynh (1997) [5] is a high-order and high-resolution method for hyperbolic conservation laws. However, the robustness of the MP scheme is not very high. In this paper, a detailed analysis on this scheme is performed, and two potential causes which may account for the weak robustness are revealed. Furthermore, in order to enhance the robustness of the MP scheme, an improved version of the MP scheme is presented, in which a strict continuous total-variation-diminishing (TVD) numerical flux is used at a disturbed discontinuity so that oscillations cannot grow indefinitely without violating the TVD condition. Without destroying the very high resolution property, numerical tests show that the improved scheme shares a strong robustness in simulating extreme numerical tests.