Fluctuating hydrodynamic methods for fluid-structure interactions in confined channel geometries

Y. WANG, H. LEI, P. J. ATZBERGER

doi:10.1007/s10483-018-2253-8

Applied Mathematics and Mechanics >

2018 , Vol. 39 >Issue 1: 125 - 152

DOI: https://doi.org/10.1007/s10483-018-2253-8

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Fluctuating hydrodynamic methods for fluid-structure interactions in confined channel geometries

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1. Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA 93106, U. S. A;
2. Pacific Northwestern National Laboratories, Richland, WA 99354, U. S. A

Received date: 2017-07-14

Revised date: 2017-08-31

Online published: 2018-01-01

Supported by

Project supported by the Applied Mathematics Program within the Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) (No. DOE ASCR CM4 DE-SC0009254), the DOE National Laboratory Directed Research Development (No. LDRD69738), and the National Science Foudation of the United States (Nos. DMS-0956210, DMS-1616353, DMR-1121053, and NSF CNS-0960316)

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Abstract

We develop computational methods for the study of fluid-structure interactions subject to thermal fluctuations when confined within channels with slit-like geometry. The methods take into account the hydrodynamic coupling and diffusivity of microstructures when influenced by their proximity to no-slip walls. We develop stochastic numerical methods subject to no-slip boundary conditions using a staggered finite volume discretization. We introduce techniques for discretizing stochastic systems in a manner that ensures results consistent with statistical mechanics. We show how an exact fluctuation-dissipation condition can be used for this purpose to discretize the stochastic driving fields and combined with an exact projection method to enforce incompressibility. We demonstrate our computational methods by investigating how the proximity of ellipsoidal colloids to the channel wall affects their active hydrodynamic responses and passive diffusivity. We also study for a large number of interacting particles collective drift-diffusion dynamics and associated correlation functions. We expect the introduced stochastic computational methods to be broadly applicable to applications in which confinement effects play an important role in the dynamics of microstructures subject to hydrodynamic coupling and thermal fluctuations.

Key words： integro-differential equation; monotone iterative technique; extremal solution; immersed boundary method; fluctuating hydrodynamics; nanochannel; stochastic Eulerian-Lagrangian method (SELM); mobility; ellipsoidal colloid

Cite this article

Y. WANG, H. LEI, P. J. ATZBERGER . Fluctuating hydrodynamic methods for fluid-structure interactions in confined channel geometries[J]. Applied Mathematics and Mechanics, 2018 , 39(1) : 125 -152 . DOI: 10.1007/s10483-018-2253-8

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