Paul Atzberger, UCSB

Stochastic Immersed Boundary Methods for Simulation of Microscopic Fluid-Structure Systems with Thermal Fluctuations.

Friday February 29th, 4pm, Phillips 332
(refreshments served in Phillips 330 starting at 3:30)

Abstract:
The immersed boundary method is a numerical approach which has been applied to many macroscopic systems involving a fluid which interacts with flexible elastic structures. For microscopic systems of sufficiently small length-scale thermal fluctuations become significant and also must be taken into account. In this talk we shall discuss an extension of the immersed boundary method framework which incorporates thermal fluctuations through appropriate stochastic forcing terms in the fluid equations. This gives a system of stiff SPDE's for which standard numerical methods perform poorly. We shall discuss a few different approaches by which stochastic calculus can be used to obtain analytic results to help in handling the stiff features of the equations. We will further show how this can be used to formulate stochastic numerical methods for the fluid-structure equations both discretized on uniform and multilevel adaptive meshes. To demonstrate the approaches in practice we shall present simulation results for some specific models motivated by applications in biophysics and complex fluids.