Splitting for Dissipative Particle Dynamics

Shardlow, Tony

doi:10.1137/s1064827501392879

Cited by 135 publications

(181 citation statements)

References 24 publications

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“…Dissipative Particle Dynamics, which has become quite popular in the soft-matter community [44][45][46][47][48][49][50][51][52][53][54][55][56], was developed to address the computational limitations of MD. A very soft interparticle potential, representing coarse-grained aggregates of molecules, enables a large time step to be used.…”

Section: Dissipative Particle Dynamics (Dpd)mentioning

confidence: 99%

Lattice Boltzmann Simulations of Soft Matter Systems

Dünweg¹,

Ladd²

2008

Advances in Polymer Science

201

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This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview of the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice-Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice-Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.

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Section: Dissipative Particle Dynamics (Dpd)mentioning

confidence: 99%

Lattice Boltzmann Simulations of Soft Matter Systems

Dünweg¹,

Ladd²

2008

Advances in Polymer Science

201

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“…-In a recent paper by Nikunen et al [4], the authors present a comparative study of the efficiency of several "novel" DPD integration schemes. The study includes, among others, the Shardlow scheme [6] and also the Lowe scheme [2]. They concluded that the Lowe scheme performs best (but it is not a discretization of the DPD equations).…”

Section: Edp Sciencesmentioning

confidence: 99%

“…Also the irreversible interactions and the conservative interactions are split and treated separately. The method has in common these two features with the Shardlow method [6]. This is different from the usual DPD discretizations where first the contributions of all pair interactions are added and subsequently the update of velocities and positions are computed.…”

Section: Edp Sciencesmentioning

confidence: 99%

Elimination of time step effects in DPD

Peters¹

2004

Europhys. Lett.

101

105

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PACS. 02.70.Ns -Molecular dynamics and particle methods. PACS. 05.40.-a -Fluctuation phenomena, random processes, noise, and Brownian motion. PACS. 66.20.+d -Viscosity of liquids; diffusive momentum transport.Abstract. -The equilibrium statistics of quantities computed by means of DPD (dissipative particle dynamics) are usually very sensitive to the time step used in the simulation. In this letter we show how to eliminate this sensitivity by considering the irreversible dynamics in DPD as the limiting case of a thermostat that leaves Maxwell-Boltzmann distribution invariant even for finite time steps. The remaining dependency on time step is solely due to the discretization of the conservative part of the dynamics and is independent of the thermostat.Introduction. -Dissipation particle dynamics (DPD) is a particle-based simulation technique. It was originally proposed to simulate fluids on a mesoscopic scale [1]. A DPD particle models a blob of atoms that have effective, soft interactions. By means of dissipative and fluctuating pair-forces, the equilibrium state of the system is made to satisfy the Boltzmann distribution. Alternatively, one can view upon DPD as a thermostatic scheme in a molecular dynamics (MD) code. In this case, the (conservative) interactions need not be soft.Because DPD is particle-based, it does not have problems associated with the use of a grid such as, e.g., lattice Boltzmann simulations. It is Galilean invariant and momentum is conserved. This is different from Brownian dynamics, Stokesian dynamics and the Andersen thermostat. Different from to the Nosé-Hoover thermostat, the DPD thermostating occurs locally in space through pair interactions. Therefore, the dynamics is expected to be more realistic.A drawback of DPD is that the results of the simulation depend on the chosen time step. None of the DPD schemes proposed up to now give the exact Boltzmann distribution when a finite time step is used. Lowe [2] has introduced a scheme that is similar to the Andersen thermostat, but considers relative velocities of nearby pairs instead of the velocity of individual particles. This scheme gives the Boltzmann distribution, even for finite time steps. It has similar characteristics as DPD, but is not equivalent. In this paper we show how to generalise the ideas of Lowe. The resulting scheme always gives correct equilibrium statistics and reduces to the DPD equations in the limit of zero time step.

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“…These concepts have been carried over to the stochastic case by constructing symplectic and quasi-symplectic integrators for stochastic Hamiltonian systems and Langevin equations (see [10,28,29,31,37]). Another branch of splitting approaches in the stochastic field (although not arising from geometric considerations) are splitstep methods, where the stochastic part is separated from the deterministic drift (see [25]).…”

Section: Splitting Methodsmentioning

confidence: 99%

Splitting Integrators for the Stochastic Landau--Lifshitz Equation

Ableidinger¹,

Buckwar²

2016

SIAM J. Sci. Comput.

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Abstract. In this article we construct splitting integrators for a finite-dimensional version of the stochastic Landau-Lifshitz equation under the influence of global and local energy terms. The methods preserve the length of the magnetization spins exactly and reproduce the energy evolution of the equation. Depending on the structure of the Hamiltonian, the methods either are explicit or contain nonlinear subsystems of small dimension, which leads to a smaller computational cost compared with standard implicit integrators. Numerical simulations are provided for evidencing convergence order and long-time behavior of the constructed methods.

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Splitting for Dissipative Particle Dynamics

Cited by 135 publications

References 24 publications

Lattice Boltzmann Simulations of Soft Matter Systems

Lattice Boltzmann Simulations of Soft Matter Systems

Elimination of time step effects in DPD

Splitting Integrators for the Stochastic Landau--Lifshitz Equation

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