Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementati...

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Bibliographic Details
Published in:Journal of computational physics Vol. 316; pp. 632 - 651
Main Authors: De Corato, M., Slot, J.J.M., Hütter, M., D'Avino, G., Maffettone, P.L., Hulsen, M.A.
Format: Journal Article
Language:English
Published: United States Elsevier Inc 01.07.2016
Subjects:
ALGORITHMS
Boundaries
Brownian motion
BROWNIAN MOVEMENT
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computational fluid dynamics
COMPUTERIZED SIMULATION
CONFINEMENT
CYLINDRICAL CONFIGURATION
DIFFERENTIAL EQUATIONS
FINITE ELEMENT METHOD
Fluctuating hydrodynamics
Fluctuation
FLUCTUATIONS
Fluid flow
FLUIDS
HARMONIC POTENTIAL
HYDRODYNAMICS
Mathematical analysis
Numerical simulations
PROBABILITY
STOCHASTIC PROCESSES
Stokes equation
Time integration
Brownian motion
Finite element method
Numerical simulations
Stokes equation
Fluctuating hydrodynamics
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2016.04.040