随机Navier-Stokes-Fourier系统蒙特卡罗方法的收敛性分析

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-06-18 DOI:10.1137/23m1563232

Mária Lukáčová-Medviďová, Bangwei She, Yuhuan Yuan

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引用次数: 0

摘要

SIAM数值分析杂志，第63卷，第3期，1254-1280页，2025年6月。摘要。本文考虑了可压缩Navier-Stokes-Fourier系统的初始数据、外力、粘度系数和导热系数作为随机数据。蒙特卡罗方法是一种常用的统计矩近似方法，它在物理空间和时间上与一种合适的确定性离散方法相结合。在假设数值密度和温度在概率上有界的情况下，应用真正的随机紧性论证证明了统计强解的随机有限体积解的收敛性。进一步，我们展示了期望和偏差的蒙特卡罗估计的收敛性和误差估计。我们给出了几个数值结果来说明理论结果。

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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Convergence Analysis of the Monte Carlo Method for the Random Navier–Stokes–Fourier System

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1254-1280, June 2025.
Abstract. In the present paper, we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier–Stokes–Fourier system. The Monte Carlo method, frequently used for approximating statistical moments, is combined with a suitable deterministic discretization method in physical space and time. Under the assumption that numerical densities and temperatures are bounded in probability, we prove the convergence of random finite volume solutions to the statistical strong solution by applying genuine stochastic compactness arguments. Further, we show the convergence and error estimates for Monte Carlo estimators of the expectation and deviation. We present several numerical results to illustrate the theoretical results.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.