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

Abstract

We develop here 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 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 approaches 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:

Plunkett, Pat ^[1]; Hu, Jonathan ^[2]; Siefert, Christopher ^[2]; Atzberger, Paul J.  ^[1]

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+ Show Author Affiliations

1. Univ. of California, Santa Barbara, CA (United States)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:

Thu Aug 07 00:00:00 EDT 2014

Research Org.:

Univ. of California, Santa Barbara, CA (United States); Lockheed Martin Corporation, Littleton, CO (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)

OSTI Identifier:

1633899

Alternate Identifier(s):

OSTI ID: 1556473

Grant/Contract Number:  

SC0009254; DMS-0956210; AC04-94AL85000

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Computational Physics

Additional Journal Information:

Journal Volume: 277; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; Stochastic Eulerian; Lagrangian method; Immersed boundary method; Adaptive numerical methods; Multigrid; Stochastic numerical methods; Stochastic partial differential equations