Eirik G. Flekkøy

Foundations of dissipative particle dynamics

We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. This procedure links the forces between the dissipative particles to a hydrodynamic description of the underlying molecular dynamics (MD) particles. In particular, the dissipative particle forces are given directly in terms of the viscosity emergent from MD, while the interparticle energy transfer is similarly given by the heat conductivity derived from MD. In linking the microscopic and mesoscopic descriptions we thus rely on the macroscopic or phenomenological description emergent from MD. Thus the rules governing this form of dissipative particle dynamics reflect the underlying molecular dynamics; in particular, all the underlying conservation laws carry over from the microscopic to the mesoscopic description. We obtain the forces experienced by the dissipative particles together with an approximate form of the associated equilibrium distribution. Whereas previously the dissipative particles were spheres of fixed size and mass, now they are defined as cells on a Voronoi lattice with variable masses and sizes. This Voronoi lattice arises naturally from the coarse-graining procedure, which may be applied iteratively and thus represents a form of renormalization-group mapping. It enables us to select any desired local scale for the mesoscopic description of a given problem. Indeed, the method may be used to deal with situations in which several different length scales are simultaneously present. We compare and contrast this particulate model with existing continuum fluid dynamics techniques, which rely on a purely macroscopic and phenomenological approach. Simulations carried out with the present scheme show good agreement with theoretical predictions for the equilibrium behavior.

FROM MOLECULAR DYNAMICS TO DISSIPATIVE PARTICLE DYNAMICS

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.

Patterns and flow in frictional fluid dynamics

Pattern-forming processes in simple fluids and suspensions have been studied extensively, and the basic displacement structures, similar to viscous fingers and fractals in capillary dominated flows, have been identified. However, the fundamental displacement morphologies in frictional fluids and granular mixtures have not been mapped out. Here we consider Coulomb friction and compressibility in the fluid dynamics, and discover surprising responses including highly intermittent flow and a transition to quasi-continuodynamics. Moreover, by varying the injection rate over several orders of magnitude, we characterize new dynamic modes ranging from stick-slip bubbles at low rate to destabilized viscous fingers at high rate. We classify the fluid dynamics into frictional and viscous regimes, and present a unified description of emerging morphologies in granular mixtures in the form of extended phase diagrams.

Coupling molecular dynamics and continuum dynamics

We present a general scheme to couple microscopic molecular-dynamics simulations to macroscopic finite-difference simulations, running concurrently in a particle domain and an adjacent continuum domain, respectively. The coupling is based on mutual flux exchange across the domain boundary.

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.

Granular Rayleigh-Taylor instability: experiments and simulations.

A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially flat front defined by the grains subsequently develops into a pattern of falling granular fingers separated by rising bubbles of air. A transient coarsening of the front is observed right from the start by a finger merging process. The coarsening is later stabilized by new fingers growing from the center of the rising bubbles. The structures are quantified by means of Fourier analysis and quantitative agreement between experiment and computation is shown. This analysis also reveals scale invariance of the flow structures under overall change of spatial scale.

Seismic stimulation for enhanced oil recovery

The pore-scale effects of seismic stimulation on two-phase flow are modeled numerically in random 2D grain0pack geometries. Seismic stimulation aims to enhance oil production by sending seismic waves across a reservoir to liberate immobile patches of oil. For seismic amplitudes above a well-defined (analytically expressed) dimensionless criterion, the force perturbation associated with the waves indeed can liberate oil trapped on capillary barriers and get it flowing again under the background pressure gradient. Subsequent coalescence of the freed oil droplets acts to enhance oil movement further because longer bubbles overcome capillary barriers more efficiently than shorter bubbles do. Poroelasticity theory defines the effective force that a seismic wave adds to the background fluid-pressure gradient. The lattice-Boltzmann model in two dimensions is used to perform pore-scale numerical simulations. Dimensionless numbers (groups of material and force parameters) involved in seismic stimulation are defined carefully so that numerical simulations can be applied to field-scale conditions. Using the analytical criteria defined in the paper, there is a significant range of reservoir conditions over which seismic stimulation can be expected to enhance oil production.

Dynamic roughening and fluctuations of dipolar chains

Nonmagnetic particles in a carrier ferrofluid acquire an effective dipolar moment when placed in an external magnetic field. This fact leads them to form chains that will roughen due to Brownian motion when the magnetic field is decreased. We study this process through experiments, theory and simulations, three methods that agree on the scaling behavior over 5 orders of magnitude. The rms width goes initially as t(1/2), then as t(1/4) before it saturates. We show how these results complement existing results on polymer chains, and how the chain dynamics may be described by a recent non-Markovian formulation of anomalous diffusion.

Lattice Boltzmann models for complex fluids

We present various lattice Boltzmann models which reproduce the effects of rough walls, shear thinning and granular flow. We examine the boundary layers generated by the roughness of the walls. Shear thinning produces plug flow with a sharp density contrast at the boundaries. Density waves are spontaneously generated when the viscosity has a nonlinear dependence on density which characterizes granular flow.

Simulating three-dimensional hydrodynamics on a cellular automata machine

We demonstrate how three-dimensional fluid flow simulations can be carried out on the Cellular Automata Machine 8 (CAM-8), a special-purpose computer for cellular automata computations. The principal algorithmic innovation is the use of a lattice gas model with a 16-bit collision operator that is specially adapted to the machine architecture. It is shown how the collision rules can be optimized to obtain a low viscosity of the fluid. Predictions of the viscosity based on a Boltzmann approximation agree well with measurements of the viscosity made on CAM-8. Several test simulations of flows in simple geometries—channels, pipes, and a cubic array of spheres-are carried out. Measurements of average flux in these geometries compare well with theoretical predictions.