Stochastic Particle Systems' Approach to Modeling of Viscous Flows

• Activity Number: 59
• Type: Invited
• Date/Time: Sunday, August 8, 2004 : 6:00 PM to 7:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Anna Amirdjanova*+
• Companies: University of Michigan
• Keywords: hydrodynamics ; particle systems ; vorticity ; stochastic partial differential equation

Abstract

For years the Navier-Stokes system has attracted special attention from researchers because of elegant and difficult problems posed by it and its fundamental importance in applications. It is well known that for large Reynolds numbers fluid flow becomes turbulent and requires a stochastic description of the model. Original idea in that direction was to study statistical solutions of the classical Navier-Stokes system. Recently, however, there's been a growing interest in the study of individual solutions to stochastic Navier-Stokes equations. There are several ways to introduce stochasticity into the system. One popular approach is to add external random forces to the classical PDE and treat it as an evolution equation in certain function spaces. Another one comes from vortex methods. The latter originate from a system of randomly moving point vortices (particles, representing centers of rotation in the fluid) and are more tractable from numerical perspective. We present our recent results on the properties of solution to stochastic vorticity equation in R^2 and comment on existing particle systems' interpretations of equations of hydrodynamics.