非守恒双曲系统的高阶单元内不连续重构路径守恒方法--DR.MOOD 方法

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Numerical Methods for Partial Differential Equations Pub Date : 2024-08-02 DOI:10.1002/num.23133

Ernesto Pimentel‐García, Manuel J. Castro, Christophe Chalons, Carlos Parés

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引用次数: 0

摘要

在这项工作中，我们开发了一个新框架，用于数值处理非守恒双曲系统中的不连续解。首先，我们介绍了基于泰勒展开的 MOOD 方法在非守恒系统中的扩展。这一扩展与单元内不连续重构算子相结合，是开发新的高阶方法系列的关键点，这些方法能够精确捕捉孤立冲击。提出了几个测试案例，以验证这些方法在修正浅水方程和两层浅水系统中的有效性。

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High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method

In this work, we develop a new framework to deal numerically with discontinuous solutions in nonconservative hyperbolic systems. First an extension of the MOOD methodology to nonconservative systems based on Taylor expansions is presented. This extension combined with an in‐cell discontinuous reconstruction operator are the key points to develop a new family of high‐order methods that are able to capture exactly isolated shocks. Several test cases are proposed to validate these methods for the Modified Shallow Water equations and the Two‐Layer Shallow Water system.

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来源期刊

Numerical Methods for Partial Differential Equations 数学-应用数学

CiteScore

7.20

自引率

2.60%

发文量

审稿时长

9 months

期刊介绍： An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.