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

Journal Article · Thu Aug 07 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2014.07.051· OSTI ID:1226084

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

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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)

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.

• Research Organization: Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 1226084
• Report Number(s): SAND-2015-9349J; 607831
• Journal Information: Journal of Computational Physics, Vol. 277, Issue C; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

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