Spatially Adaptive Stochastic Methods for Fluid-Structure Interactions Subject to Thermal Fluctuations in Domains with Complex Geometries

摘要

We develop stochastic mixed finite element methods for spatially adaptivesimulations of fluid-structure interactions when subject to thermalfluctuations. To account for thermal fluctuations, we introduce a discretefluctuation-dissipation balance condition to develop compatible stochasticdriving fields for our discretization. We perform analysis that shows ourcondition is sufficient to ensure results consistent with statisticalmechanics. We show the Gibbs-Boltzmann distribution is invariant under thestochastic dynamics of the semi-discretization. To generate efficiently therequired stochastic driving fields, we develop a Gibbs sampler based oniterative methods and multigrid to generate fields with $O(N)$ computationalcomplexity. Our stochastic methods provide an alternative to uniformdiscretizations on periodic domains that rely on Fast Fourier Transforms. Todemonstrate in practice our stochastic computational methods, we investigatewithin channel geometries having internal obstacles and no-slip walls how themobility/diffusivity of particles depends on location. Our methods extend theapplicability of fluctuating hydrodynamic approaches by allowing for spatiallyadaptive resolution of the mechanics and for domains that have complexgeometries relevant in many applications.