Twin Brownian Particle Method for the Study of Oberbeck-Boussinesq Fluid Flows
发布时间：2024年03月26日
浏览次数：1029
发布者: He Liu
主讲人： Jiawei Li(University of Edinburgh)
活动时间： 从 2024-04-10 16:00 到 17:30
场地： 线上
We establish stochastic functional integral representations for solutions of Oberbeck-Boussinesq equations in the form of McKean-Vlasov-type mean field equations, which can be used to design numerical schemes for calculating solutions and implementing Monte-Carlo simulations of Oberbeck-Boussinesq flows. Our approach is based on the duality of conditional laws for a class of diffusion processes associated with solenoidal vector fields, which allows us to obtain a novel integral representation theorem for the solution of some linear parabolic equation in terms of the Green function and the pinned measure of the associated diffusion. We demonstrate via numerical experiments the efficiency of the numerical schemes, which are capable of revealing numerically the details of Oberbeck-Boussinesq flows within their thin boundary layer, including Benard's convection feature.
This is based on a joint work with Zhongmin Qian and Mingyu Xu: https://arxiv.org/abs/2303.17260
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