Mar Serrano

Incompressible smoothed particle hydrodynamics

We present a smoothed particle hydrodynamic model for incompressible fluids. As opposed to solving a pressure Poisson equation in order to get a divergence-free velocity field, here incompressibility is achieved by requiring as a kinematic constraint that the volume of the fluid particles is constant. We use Lagrangian multipliers to enforce this restriction. These Lagrange multipliers play the role of non-thermodynamic pressures whose actual values are fixed through the kinematic restriction. We use the SHAKE methodology familiar in constrained molecular dynamics as an efficient method for finding the non-thermodynamic pressure satisfying the constraints. The model is tested for several flow configurations.

Fluctuating hydrodynamic modeling of fluids at the nanoscale

A good representation of mesoscopic fluids is required to combine with molecular simulations at larger length and time scales [De Fabritiis, Phys. Rev. Lett. 97, 134501 (2006)]. However, accurate computational models of the hydrodynamics of nanoscale molecular assemblies are lacking, at least in part because of the stochastic character of the underlying fluctuating hydrodynamic equations. Here we derive a finite volume discretization of the compressible isothermal fluctuating hydrodynamic equations over a regular grid in the Eulerian reference system. We apply it to fluids such as argon at arbitrary densities and water under ambient conditions. To that end, molecular dynamics simulations are used to derive the required fluid properties. The equilibrium state of the model is shown to be thermodynamically consistent and correctly reproduces linear hydrodynamics including relaxation of sound and shear modes. We also consider nonequilibrium states involving diffusion and convection in cavities with no-slip boundary conditions.

THERMODYNAMICALLY ADMISSIBLE FORM FOR DISCRETE HYDRODYNAMICS

We construct a discrete model of fluid particles according to a two generator formalism for nonequilibrium thermodynamics. The model has the form of smoothed particle hydrodynamics including correct thermal fluctuations. A slight variation of the model reproduces the dissipative particle dynamics model with any desired thermodynamic behavior. The resulting algorithms have the following properties: mass, momentum, and energy are conserved, entropy is a nondecreasing function of time, and the thermal fluctuations produce the correct Einstein distribution function at equilibrium.

A stochastic Trotter integration scheme for dissipative particle dynamics

In this article we show in detail the derivation of an integration scheme for the dissipative particle dynamic model (DPD) using the stochastic Trotter formula [G. De Fabritiis, M. Serrano, P. Espanol, P.V. Coveney, Phys. A 361 (2006) 429]. We explain some subtleties due to the stochastic character of the equations and exploit analyticity in some interesting parts of the dynamics. The DPD-Trotter integrator demonstrates the inexistence of spurious spatial correlations in the radial distribution function for an ideal gas equation of state. We also compare our numerical integrator to other available DPD integration schemes.

Mesoscopic dynamics of Voronoi fluid particles

We compare and contrast two recently reported mesoscopic fluid particle models based on a two-dimensional Voronoi tessellation. Both models describe a Newtonian fluid at mesoscopic scales where fluctuations are important. From the requirement of thermodynamic consistency, the equilibrium distribution function is given through the Einstein distribution function. We compute from the Einstein distribution the equilibrium distribution function for a single fluid particle. We observe excellent agreement between the simulation results for the proposed models and the theoretical distribution function.

Efficient numerical integrators for stochastic models

The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability.

Markovian approximation in a coarse-grained description of atomic systems

The Markovian assumption stating that memory effects can be neglected is a crucial assumption in the theory of coarse-graining. We investigate the coarse-graining of a one-dimensional chain of oscillators where the atoms are grouped into clusters or blobs. When the interaction between oscillators is through Hookean springs, the cluster dynamics is non-Markovian, as has been recently noted by Cubero and Yaliraki [J. Chem. Phys. 122, 03418 (2005)]. When the oscillators interact through a nonlinear potential of the Lennard-Jones type, the dynamics turns out to be Markovian. The different behavior in both types of interactions is attributed to the persistence of sound waves in the harmonic case, which are strongly suppressed in the nonlinear case.

Response to “Comment on ‘Markovian approximation in a coarse-grained description of atomic systems’ ” [J. Chem. Phys. 128, 147101 (2008)]

We show within the Mori theory of projection operators that the Green-Kubo formula using microscopic rather than projected forces is only valid if the description is Markovian. Therefore, the only way to assess whether a description is Markovian is through examining the predictions of the theory under the Markovian assumption. Although, in principle, the blob description for a unidimensional chain is non-Markovian, in practice the Markovian approximation describes reasonably well the coarse dynamics of the chain.

Collective effects in dissipative particle dynamics

We study the detailed dynamics of DPD particles by looking at the velocity autocorrelation function. We observe that in the regimes of interest for simulations, the velocity autocorrelation function reflects the hydrodynamic behavior of these particles.