Numerical approximation of the stochastic Navier–Stokes equations through artificial compressibility

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-06 DOI:10.1007/s10092-024-00575-3

引用次数: 0

Abstract

A constructive numerical approximation of the two-dimensional unsteady stochastic Navier–Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a penalty parameter \(\varepsilon \) . Space and time are discretized through a finite element approximation and an Euler method. The convergence analysis of the suggested numerical scheme is investigated throughout this paper. It is based on a local monotonicity property permitting the convergence toward the unique strong solution of the stochastic Navier–Stokes equations to occur within the originally introduced probability space.

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通过人工可压缩性对随机纳维-斯托克斯方程进行数值逼近

摘要通过涉及惩罚参数 \(\varepsilon \)的伪可压缩性技术，提出了不可压缩流体的二维非稳态随机纳维-斯托克斯方程的建设性数值近似。通过有限元近似和欧拉方法对空间和时间进行离散。本文通篇研究了建议数值方案的收敛性分析。它基于局部单调性特性，允许在最初引入的概率空间内向随机纳维-斯托克斯方程的唯一强解收敛。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.