On the stability of strong-stability-preserving modified Patankar–Runge–Kutta schemes

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2023-03-01 DOI:10.1051/m2an/2023005

Juntao Huang, Thomas Izgin, Stefan Kopecz, Andreas Meister, Chi-Wang Shu

引用次数: 3

Abstract

In this paper, we perform a stability analysis for classes of second and third order accurate strong-stability-preserving modified Patankar–Runge–Kutta (SSPMPRK) schemes, which were introduced in Huang and Shu [ J. Sci. Comput. 78 (2019) 1811–1839] and Huang et al . [ J. Sci. Comput. 79 (2019) 1015–1056] and can be used to solve convection equations with stiff source terms, such as reactive Euler equations, with guaranteed positivity under the standard CFL condition due to the convection terms only. The analysis allows us to identify the range of free parameters in these SSPMPRK schemes in order to ensure stability. Numerical experiments are provided to demonstrate the validity of the analysis.

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强保稳修正Patankar-Runge-Kutta方案的稳定性

本文对Huang和Shu [J. Sci.]提出的二阶和三阶精确强保持修正Patankar-Runge-Kutta (SSPMPRK)格式进行了稳定性分析。计算机学报，78(2019)1811-1839]。[j]。计算。79(2019)1015-1056]，可用于求解具有刚性源项的对流方程，如反应性欧拉方程，在标准CFL条件下，仅由于对流项而保证正性。分析使我们能够确定这些SSPMPRK方案的自由参数范围，以确保稳定性。数值实验验证了分析的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

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