We establish stochastic functional integral representations for incompressible fluid flows occupying wall-bounded domains using the conditional law duality for a class of diffusion processes. These representations are used to derive a Monte-Carlo scheme based on the corresponding exact random vortex formulation. We implement several numerical experiments based on the Monte-Carlo method without appealing to the boundary layer flow computations, to demonstrate the methodology.

翻译：我们利用一类扩散过程的条件律对偶性，建立了占据有界壁面区域的不可压缩流体流动的随机泛函积分表示。这些表示被用于推导基于相应精确随机涡量公式的蒙特卡洛方案。我们基于蒙特卡洛方法实施了几项数值实验，无需借助边界层流动计算，以展示该方法。