Stability and temporal error estimate of scalar auxiliary variable schemes for the magnetohydrodynamics equations with variable density

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Numerical Methods for Partial Differential Equations Pub Date : 2023-08-28 DOI:10.1002/num.23067

Han Chen, Yuyu He, Hongtao Chen

引用次数: 0

Abstract

In this article, we construct first‐ and second‐order semidiscrete schemes for the magnetohydrodynamics (MHD) equations with variable density based on scalar auxiliary variable (SAV) approach. These schemes are decoupled, unconditionally energy stable and only solve a sequence of linear differential equations at each time step. We carry out a rigorous error analysis for the first‐order SAV scheme in two‐dimensional case. Some numerical experiments are presented to verify the accuracy and stability.

查看原文本刊更多论文

变密度磁流体动力学方程标量辅助变量格式的稳定性和时间误差估计

本文基于标量辅助变量(SAV)方法，构造了变密度磁流体动力学(MHD)方程的一阶和二阶半离散格式。这些格式是解耦的，无条件能量稳定的，并且在每个时间步只求解一系列线性微分方程。我们对二维情况下的一阶SAV格式进行了严格的误差分析。通过数值实验验证了该方法的准确性和稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.