SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Multiscale Problems in Fluctuating Hydrodynamics

A. Donev and E. Vanden-Eijnden

Abstract
Thermal fluctuations have been incorporated into the classical equations of fluid dynamics, however, the resulting systems of stochastic PDEs are very difficult to handle. I will focus on the problem of diffusive mixing of fluids, and demonstrate that accounting for the spectrum of the thermal velocity fluctuations is crucial in simulating even the simplest diffusive processes in realistic liquids. Comparisons between hard-particle molecular dynamics and fluctuating hydrodynamics finite-volume solvers show a good agreement. Due to extreme time scale separation between mass and momentum diffusion (a factor of 400 in water, for example), even finite-volume simulations become impractical. It is therefore necessary to use a seamless multiscale method to reduce the stiffness, or to directly model the limiting dynamics obtained from adiabatic mode elimination. I will describe and compare these approaches both analytically and numerically.

Organized by         Universidad de Valladolid     IMUVA