强保稳修正Patankar-Runge-Kutta方案的稳定性

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

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引用次数: 3

摘要

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。

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

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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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

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.