论文标题
壁界区域中不可压缩流体流的随机配方
Stochastic formulation of incompressible fluid flows in wall bounded regions
论文作者
论文摘要
在本文中，我们建立了一个数学框架，该框架可用于设计蒙特卡罗模拟，以用于一类不可逆的动态系统，例如不可压缩的流体流，包括壁挂式区域中的湍流以及其他一些（非线性）动态系统。 Path integral representations for solutions of forward parabolic equations are obtained, and, in combining with the vorticity transport equations, probabilistic formulations for solutions of the Navier-Stokes equations are therefore derived in terms of (forward) McKean-Vlasov stochastic differential equations (SDEs), which provides us with the mathematical framework for Monte-Carlo simulations of wall-bounded turbulent flows.
In this paper we establish a mathematical framework which may be used to design Monte-Carlo simulations for a class of time irreversible dynamic systems, such as incompressible fluid flows, including turbulent flows in wall-bounded regions, and some other (non-linear) dynamic systems. Path integral representations for solutions of forward parabolic equations are obtained, and, in combining with the vorticity transport equations, probabilistic formulations for solutions of the Navier-Stokes equations are therefore derived in terms of (forward) McKean-Vlasov stochastic differential equations (SDEs), which provides us with the mathematical framework for Monte-Carlo simulations of wall-bounded turbulent flows.
