## UC Berkeley / Lawrence Berkeley Laboratory

#### Finite volume methods for fluctuating hydrodynamics

**John Bell, Lawrence Berkeley Laboratory**

##### November 9th, 2011 at 4PM–5PM in 939 Evans Hall [Map]

At small scales, the Navier–Stokes equations traditionally used for modeling
fluid flow 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
adds 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 PDEs with
stochastic flux terms.

A key element in the construction of the numerical methods is designing
discretizations that satisfy a discrete fluctuation-dissipation principle. We
introduce a systematic approach based on studying discrete equilibrium
structure factors (spectra) as a function of wavenumber and frequency. Within
this framework we then discuss the construction of explicit discretizations for
miscible fluid mixtures. Finally, we present results on giant fluctuations in
diffusively-mixing fluids and discuss the role of fluctuations in the
construction of hybrid atomistic/continuum algorithms.