Between Kinetic Theory and Navier Stokes - Modeling Fluids at the Mesoscale

Abstract:

At small scales, the Navier-Stokes equations traditionally used for uid modeling break down and thermal uctuations play an important role in the dynamics. Landau and Lifshitz proposed a modified version of the Navier-Stokes equations, referred to as uctuating hydrodynamics (FHD) that incorporates stochastic ux terms designed to represent the effect of uctuations. These stochastic fluxes are constructed so that the FHD equations are consistent with equilibrium fluctuations from statistical mechanics. Here we introduce the FHD equations for low Mach number models of multicomponent mixtures, then discuss the development and analysis of finite-volume methods for solving the resulting equations. We also discuss generalizations required to model chemical reactions and electrolytes. We present numerical results that validate the methodology and illustrate the impact of uctuations on systems out of equilibrium.

Biography:

John Bell is a Senior Scientist at Lawrence Berkeley National Laboratory and Chief Scientist of Berkeley Lab’s Computational Research Division.   His research focuses on the development and analysis of numerical methods for partial differential equations arising in science and engineering. He has made contributions in the areas of finite volume methods, numerical methods for low Mach number flows, adaptive mesh refinement, stochastic differential equations, interface tracking and parallel computing. He has also worked on the application of these numerical methods to problems from a broad range of fields, including combustion, shock physics, seismology, atmospheric flows, flow in porous media, mesoscale fluid modeling and astrophysics.  He is a Fellow of the Society of Industrial and Applied Mathematics and a member of the National Academy of Sciences.