CSE Distinguished Seminar | John Bell

Abstract

At small scales, the Navier-Stokes equations traditionally used for fluid modeling break down and thermal fluctuations play an important role in the dynamics. Landau and Lifshitz proposed a modified version of the Navier-Stokes equations, referred to as the fluctuating Navier-Stokes equations (FNS) that incorporates stochastic flux terms designed to incorporate the effect of fluctuations. These stochastic fluxes are constructed so that the FNS equations are consistent with equilibrium fluctuations from statistical mechanics. Here we describe the development and analysis of finite-volume methods for solving the equations of fluctuating hydrodynamics for miscible fluid mixtures. We focus on low Mach number models for multicomponent systems and discuss generalizations to include chemical reactions and charged fluids. We present numerical results that validate the methodology and illustrate the impact of fluctuations on systems out of equilibrium.