Dissipative particle dynamics with energy conservation

Ávalos, Josep Bonet; Mackie, Allan D.

doi:10.1209/epl/i1997-00436-6

Cited by 182 publications

(140 citation statements)

References 14 publications

(27 reference statements)

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“…[47], where the conservative forces were derived from a free energy function. In order to deal with non-isothermal situations, energy conserving DPD (EDPD) was introduced by including an internal energy for the dissipative particles [48][49] . In order to have better representations of the friction forces and angular momentum conservation, the fluid particle model (FPM) was introduced in Refs.…”

Section: What Is Sdpd?mentioning

confidence: 99%

Everything you always wanted to know about SDPD⋆ (⋆but were afraid to ask)

Ellero

Español

2017

Appl. Math. Mech.-Engl. Ed.

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Section: What Is Sdpd?mentioning

confidence: 99%

Everything you always wanted to know about SDPD⋆ (⋆but were afraid to ask)

Ellero

Español

2017

Appl. Math. Mech.-Engl. Ed.

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“…The minimum of the residual corresponds to the following relationship: (10) where M is the FE mass matrix, with dimensions 3N × 3N, expressed as (11) Since the basic assumption of the mesoscale discretization relies on the Voronoi tesselation of space, the matrix M represents the finite element consistent mass matrix M, i.e., (12) where ρ is the fluid density, V is the element volume, and N(ξ 1 , ξ 2 , ξ 3 ) is the matrix of interpolation functions of order 3N × 3N, evaluated at material points continuously distributed within the finite element. From the relation (10) we obtain (13) Substituting (13) into (5) and then into (4), we obtain the fine scale velocity correction v′ as (14) expressed in terms of the fine scale (mesoscale) velocity v. This equation can be written as (15) where (16) and (17) are the projection operators, and I is the identity matrix. We note that dimensions of the projection operators P and Q are 3n a × 3n a .…”

Section: Decomposition Of Velocitiesmentioning

confidence: 99%

“…The Lagrangian description of motion employed in the DP methods assumes appropriate quantification of interaction forces, which include conservative, dissipative and random forces (and moments). One of the most advanced methods in this field is the dissipative particle dynamics (DPD) method for fluids, introduced by Hoogerbrugge and Koelman [6], further generalized theoretically, particularly by Espanol and co-authors [7][8][9][10][11][12][13][14][15][16], Flekkoy and co-authors [2,3], and in [17][18][19], and applied to various problems [20][21][22][23][24]. The DPD method will be described here in some detail and used subsequently.…”

Section: Introductionmentioning

confidence: 99%

A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method

Kojić

Filipović

Tsuda

2008

Computer Methods in Applied Mechanics and Engineering

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A multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study. We call this procedure the mesoscopic bridging scale (MBS) method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models [G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249-274]. We derive the governing equations of the MBS method and show that the differential equations of motion of the mesoscale discrete particle model and finite element (FE) model are only coupled through the force terms. Based on this coupling, we express the finite element equations which rely on the Navier-Stokes and continuity equations, in a way that the internal nodal FE forces are evaluated using viscous stresses from the mesoscale model. The dissipative particle dynamics (DPD) method for the discrete particle mesoscale model is employed. The entire fluid domain is divided into a local domain and a global domain. Fluid flow in the local domain is modeled with both DPD and FE method, while fluid flow in the global domain is modeled by the FE method only.The MBS method is suitable for modeling complex (colloidal) fluid flows, where continuum methods are sufficiently accurate only in the large fluid domain, while small, local regions of particular interest require detailed modeling by mesoscopic discrete particles. Solved examplessimple Poiseuille and driven cavity flows illustrate the applicability of the proposed MBS method. KeywordsMultiscale modeling of fluid flow; Mesoscopic bridging scale method; Dissipative particle dynamics method; Finite element method; Coupling Navier; Stokes and dissipative particle dynamics equations

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“…(4). The isothermal results, adapted to the present case, are the fluctuation dissipation relations ω 2 kl = 2ω 2 kl⊥ = 4ηk B T (l kl /r kl ) for the forceF kl and for the heat fluctuations Λ 2 kl = 2k B T λ(l kl /r kl ) [16]. It is also possible to show that detailed balance [18] holds, and that the DP's obey the Gibbs distribution [12] …”

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confidence: 93%

“…[8,12,16] the magnitudes ofF kl andq kl are obtained on the basis of the Fokker-Planck equation which derives from equations like Eqs. (4).…”

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confidence: 99%

From Molecular Dynamics to Dissipative Particle Dynamics

1999

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A procedure is introduced for deriving a coarse-grained dissipative particle dynamics from molecular dynamics. The rules of the dissipative particle dynamics are derived from the underlying molecular interactions, and a Langevin equation is obtained that describes the forces experienced by the dissipative particles and specifies the associated canonical Gibbs distribution for the system. The basic components of DPD are particles that are thought to represent mesoscopic elements of the underlying molecular fluid. These dissipative particles then evolve just as MD particles but with different interparticle forces: Since the DPD particles are pictured as having internal degrees of freedom, the forces between them have both a fluctuating and a dissipative component in addition to the conservative forces that are present already at the MD level. Nevertheless, momentum conservation along with mass conservation produce hydrodynamic behavior at the macroscopic level.Dissipative particle dynamics has been demonstrated to connect correctly to the macroscopic continuum theory; that is, for a one-component DPD fluid, it is possible to derive the Navier-Stokes equations and to compute the viscosity in the large scale limit [8,9]. However, thus far no attempt has been made to link DPD to the underlying microscopic dynamics. This is the purpose of the present letter. We define the dissipative particles (DP) by appropriate weight functions that sample a portion of the underlying conservative MD particles, and we derive the forces between the DP's from the hydrodynamic description of the MD system. The dissipative particles are defined as cells in the Voronoi lattice, moving with velocity U k . There are four relevant length scales: The scale of the large, gray colloid particles, the two scales of the dissipative particles in between and away from the colloids and finally the scale of the MD particles, which are shown as the little dots that form the boundaries between the DP's.

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Dissipative particle dynamics with energy conservation

Cited by 182 publications

References 14 publications

Everything you always wanted to know about SDPD⋆ (⋆but were afraid to ask)

Everything you always wanted to know about SDPD⋆ (⋆but were afraid to ask)

A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method

From Molecular Dynamics to Dissipative Particle Dynamics

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