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 modifi ed version of the Navier-Stokes equations for single component systems, referred to as the fluctuating Navier-Stokes equations (FNS), that incorporates stochastic flux terms designed to capture the eff ect of fluctuations. These stochastic fluxes are constructed so that the FNS equations are consistent with equilibrium fluctuations from statistical mechanics. In this talk, we discuss how to extend the FNS equations to more general multicomponent systems. The starting point for this development is the entropy production for a mixture, which establishes the form of the thermodynamic forces and fluxes. We then use the fluctuation-dissipation principle to formulate the corresponding noise terms. We will discuss numerical methods for the resulting system of stochastic partial di differential equations. First, we consider explicit nite volume discretizations for the full compressible version of the system. Next we discuss how to construct low Mach number approximations that avoid an acoustic time step restriction. Finally, we present numerical results illustrating the impact of fluctuations in non-equilibrium settings.
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