Title：Stochastic methods in computational fluiddynamics and turbulence
Speaker：Zhongmin Qian（Oxford University）
Time：Friday, April 7, 15:00-17:00
Location：Tencent Meeting，Meeting ID：893 4129 1815
Abstract：In these talks I am going to present a small part of the science suggested inthe title, and I aim to cover some ideas of applying stochastic calculus to Computational Fluid Dynamics (CFD) which are developed recently by various authors including some of my coauthors and myself: Prof. Endre Süli (Oxford), Prof. Youchun Qiu (Toulouse, France), Profianglun Wu (Swansea), Prof. Mingyu Xu (Fudan), Dr Jiawei Li (Edinburgh), Mr YihuangZhang (Oxford Dphil student), based on the following papers:
1. Tracking the vortex motion by using Brownian fluid particles, Phys. Fluids 33, 105113 (2021).
2. McKean-Vlasov type stochastic differential equations arising from the random vortex method Partial Differential Equations and Applications (2022) 3:7
3. Random vortex dynamics via functional stochastic differential equations. Proc. R. Soc. A 478: 70270030.
4. https://arxi.org/pdf/2206.05198.pdf
5.https://arxiw.org pdf/230317260.pdf
Lecture 1: In this talk I will explain the idea how to formulate (income-pressible) fluid dynamic equations into McKean-Vlasov type mean filed equations, and outline some Mathematical questions which may be worthy to explore. As an example, I will present a new methodfor solving a related McKean-Vlasov SDEs by means of weak solution method.
Lecture 2: In this talk I will first establish the duality of conditional laws among diffusionprocesses associated with solenoidal vector fields, and establish new functional integral representtation theorem for a class of linear (but temporal non-homogeneous) parabolic equationsFinally we apply the new representation theorem for the study of incompressible fluid flowspast a solid wall.
More information about HIT-WHU Seminar on Stochastic Analysis and Algorithms can be found here.
