一种新的可证明稳定的加权状态再分配算法

IF 3 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Scientific Computing Pub Date : 2024-09-04 DOI:10.1137/23m1597484

Marsha Berger, Andrew Giuliani

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引用次数: 0

摘要

SIAM 科学计算期刊》，第 46 卷第 5 期，第 A2848-A2873 页，2024 年 10 月。摘要我们提出了一种使用状态重分布的切割单元有限体积实用方法。我们的算法在很多情况下都能证明是单调的、总变异递减的和 GKS（Gustafsson, Kreiss, Sundström）稳定的，并能在切割单元大小接近目标值时连续关闭。我们的分析揭示了原始状态重分布如此有效的原因：它为大多数配置带来了单调方案，尽管有时会受到稍小的 CFL 条件的限制。我们的分析还解释了为什么预合并步骤是有益的。我们展示了二维和三维的计算实验。

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A New Provably Stable Weighted State Redistribution Algorithm

SIAM Journal on Scientific Computing, Volume 46, Issue 5, Page A2848-A2873, October 2024.
Abstract. We propose a practical finite volume method on cut cells using state redistribution. Our algorithm is provably monotone, total variation diminishing, and GKS (Gustafsson, Kreiss, Sundström) stable in many situations, and shuts off continuously as the cut cell size approaches a target value. Our analysis reveals why original state redistribution works so well: it results in a monotone scheme for most configurations, though at times subject to a slightly smaller CFL condition. Our analysis also explains why a premerging step is beneficial. We show computational experiments in two and three dimensions.

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来源期刊

SIAM Journal on Scientific Computing 数学-应用数学

CiteScore

5.50

自引率

3.20%

发文量

209

审稿时长

1 months

期刊介绍： The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems. SISC papers are classified into three categories: 1. Methods and Algorithms for Scientific Computing: Papers in this category may include theoretical analysis, provided that the relevance to applications in science and engineering is demonstrated. They should contain meaningful computational results and theoretical results or strong heuristics supporting the performance of new algorithms. 2. Computational Methods in Science and Engineering: Papers in this section will typically describe novel methodologies for solving a specific problem in computational science or engineering. They should contain enough information about the application to orient other computational scientists but should omit details of interest mainly to the applications specialist. 3. Software and High-Performance Computing: Papers in this category should concern the novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis, or visualization. The primary focus should be on computational methods that have potentially large impact for an important class of scientific or engineering problems.