We develop a numerical method for simulation of incompressible viscous flows by integrating the technology of random vortex method with the core idea of Large Eddy Simulation (LES). Specifically, we utilize the filtering method in LES, interpreted as spatial averaging, along with the integral representation theorem for parabolic equations, to achieve a closure scheme which may be used for calculating solutions of Navier-Stokes equations. This approach circumvents the challenge associated with handling the non-locally integrable 3-dimensional integral kernel in the random vortex method and facilitates the computation of numerical solutions for flow systems via Monte-Carlo method. Numerical simulations are carried out for both laminar and turbulent flows, demonstrating the validity and effectiveness of the method.

翻译：我们通过将随机涡方法技术与大涡模拟（LES）的核心思想相结合，开发了一种用于模拟不可压缩粘性流动的数值方法。具体而言，我们利用LES中被解释为空间平均的滤波方法，以及抛物型方程的积分表示定理，实现了一种可用于计算Navier-Stokes方程解的闭合方案。该方法规避了随机涡方法中处理非局部可积三维积分核的挑战，并通过Monte-Carlo方法促进了流动系统数值解的计算。对层流和湍流均进行了数值模拟，结果验证了该方法的有效性和可行性。