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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 also 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. Furthermore, 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.
 [1] ;  [2] ;  [2] ;  [1]
  1. Univ. of California, Santa Barbara, CA (United States)
  2. Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Sandia National Laboratories, Albuquerque, NM (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0021-9991; 607831
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 277; Journal Issue: C
Research Org:
Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Sandia National Laboratories, Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Stochastic Eulerian Lagrangian method; Immersed boundary method; Adaptive numerical methods; multigrid; Stochastic numerical methods; Stochastic partial differential equations