Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics

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• 作者：Thomas Y. Hou ; Wuan Luo ; Boris Rozovskii and Hao-Min Zhou
• 关键词：Wiener Chaos expansions ; Stochastic differential equations ; Numerical methods ; Navier– ; Stokes equations
• 刊名：Journal of Computational Physics
• 出版年：2006
• 出版时间：10 August 2006
• 年：2006
• 卷：216
• 期：2
• 页码：687-706
• 全文大小：482 K

文摘

In this paper, we propose a numerical method based on Wiener Chaos expansion and apply it to solve the stochastic Burgers and Navier–Stokes equations driven by Brownian motion. The main advantage of the Wiener Chaos approach is that it allows for the separation of random and deterministic effects in a rigorous and effective manner. The separation principle effectively reduces a stochastic equation to its associated propagator, a system of deterministic equations for the coefficients of the Wiener Chaos expansion. Simple formulas for statistical moments of the stochastic solution are presented. These formulas only involve the solutions of the propagator. We demonstrate that for short time solutions the numerical methods based on the Wiener Chaos expansion are more efficient and accurate than those based on the Monte Carlo simulations.