Stochastic methods in computational fluiddynamics and turbulence

Release time:2023-04-04Views:307

Title:Stochastic methods in computational fluiddynamics and turbulence

Speaker:Zhongmin Qian(Oxford University

Time:Friday, April 7, 15:00-17:00

Location:Tencent MeetingMeeting 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.


5. 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.

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