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Title: Spatially adaptive stochastic methods for fluid–structure interactions subject to thermal fluctuations in domains with complex geometries

We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid–structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation–dissipation balance condition to develop compatible stochastic driving fields for our discretization. We perform analysis that shows our condition is sufficient to ensure results consistent with statistical mechanics. We show the Gibbs–Boltzmann distribution is invariant under the stochastic dynamics of the semi-discretization. To generate efficiently the required stochastic driving fields, we develop a Gibbs sampler based on iterative methods and multigrid to generate fields with O(N) computational complexity. Our stochastic methods provide an alternative to uniform discretizations on periodic domains that rely on Fast Fourier Transforms. To demonstrate in practice our stochastic computational methods, we investigate within channel geometries having internal obstacles and no-slip walls how the mobility/diffusivity of particles depends on location. Our methods extend the applicability of fluctuating hydrodynamic approaches by allowing for spatially adaptive resolution of the mechanics and for domains that have complex geometries relevant in many applications.
Authors:
 [1] ; ;  [2] ;  [1]
  1. University of California, Department of Mathematics, Santa Barbara, CA 93106 (United States)
  2. Sandia National Laboratories (United States)
Publication Date:
OSTI Identifier:
22382143
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 277; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOLTZMANN STATISTICS; FINITE ELEMENT METHOD; FLUCTUATIONS; FLUIDS; ITERATIVE METHODS; LAGRANGIAN FUNCTION; MOBILITY; PARTIAL DIFFERENTIAL EQUATIONS; PERIODICITY; RESOLUTION; SLIP; STATISTICAL MECHANICS; STOCHASTIC PROCESSES