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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Vydáno v:	Journal of computational physics Ročník 316; s. 632 - 651
Hlavní autoři:	De Corato, M., Slot, J.J.M., Hütter, M., D'Avino, G., Maffettone, P.L., Hulsen, M.A.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	United States Elsevier Inc 01.07.2016
Témata:	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
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Abstract	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.
AbstractList	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. 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.
Author	Slot, J.J.M. Hütter, M. Hulsen, M.A. D'Avino, G. Maffettone, P.L. De Corato, M.
Author_xml	– sequence: 1 givenname: M. orcidid: 0000-0002-9361-4794 surname: De Corato fullname: De Corato, M. email: marco.decorato@unina.it organization: Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli, Italy – sequence: 2 givenname: J.J.M. surname: Slot fullname: Slot, J.J.M. email: j.j.m.slot@tue.nl organization: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands – sequence: 3 givenname: M. orcidid: 0000-0002-8161-9002 surname: Hütter fullname: Hütter, M. email: m.huetter@tue.nl organization: Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands – sequence: 4 givenname: G. surname: D'Avino fullname: D'Avino, G. email: gadavino@unina.it organization: Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli, Italy – sequence: 5 givenname: P.L. surname: Maffettone fullname: Maffettone, P.L. email: pierluca.maffettone@unina.it organization: Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli, Italy – sequence: 6 givenname: M.A. surname: Hulsen fullname: Hulsen, M.A. email: m.a.hulsen@tue.nl organization: Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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Snippet	In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles....
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SubjectTerms	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
Title	Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes
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