Introduction

My research focuses broadly on simulations of multi-phase flows and on the theory required to develop such numerical methods. The first method of choice are lattice Boltzmann simulations, often in combination with local thermodynamic descriptions.

More recently we have focused on deriving such lattice Boltzmann methods from more fundamental microscopic methods. Examples include mapping an Ising model onto lattice Boltzmann or using Molecular Dynamics as the fundamental underpinning.

Lattice Boltzmann methods for multiphase flows

My group has been working on a number of interesting multi-phase flow phenomena from phase separation fronts to evaporation phenomena. Some relevant papers are:

Phase separation fronts:

Enslaved phase-separation fronts in one-dimensional binary mixturesPhase-separation fronts leave in their wakes morphologies that are substantially different from the morphologies formed in homogeneous phase separation. In this paper we focus on fronts in binary mixtures that are enslaved phase-separation fronts, i.e., fronts that follow in the wake of a control-parameter front. In the one-dimensional case, which is the focus of this paper, the formed morphology is deceptively simple: alternating domains of a regular size. However, determining the size of these domains as a function of the front speed and other system parameters is a nontrivial problem. We present an analytical solution for the case where no material is deposited ahead of the front and numerical solutions and scaling arguments for more general cases. Through these enslaved phase-separation fronts large domains can be formed that are practically unattainable in homogeneous one-dimensional phase separation.

Survey of morphologies formed in the wake of an enslaved phase-separation front in two dimensionsA phase-separation front will leave in its wake a phase-separated morphology that differs markedly from homogeneous phase-separation morphologies. For a purely diffusive system such a front, moving with constant velocity, will generate very regular, nonequilibrium structures. We present here a numerical study of these fronts using a lattice Boltzmann method. In two dimensions these structures are regular stripes or droplet arrays. In general the kind and orientation of the selected morphology and the size of the domains depends on the speed of the front as well as the composition of the material overtaken by the phase-separation front. We present a survey of morphologies as a function of these two parameters. We show that the resulting morphologies are initial condition dependent. We then examine which of the potential morphologies is the most stable. An analytical analysis for symmetrical compositions predicts the transition point from orthogonal to parallel stripes.

Integer lattice gas methods

Lattice Boltzmann methods were originally derived from lattice gas methods. These methods are surprisingly simple: particles on a lattice will collide when they are on the same lattice site conserving mass an momentum. Original lattice gases had single occupation numbers for each particle velocity, but integer lattice gases relax this restriction.

While most modern lattice Boltzmann methods cannot be derived from lattice gases (as is immediately obvious from the fact that they can become unstable) integer lattice gases have the entropic lattice Boltzmann method as their Boltzmann limit.

Integer lattice gas with Monte Carlo collision operator recovers the lattice Boltzmann method with Poisson-distributed fluctuationsWe examine a new kind of lattice gas that closely resembles modern lattice Boltzmann methods. This new kind of lattice gas, which we call a Monte Carlo lattice gas, has interesting properties that shed light on the origin of the multirelaxation time collision operator, and it derives the equilibrium distribution for an entropic lattice Boltzmann. Furthermore these lattice gas methods have Galilean invariant fluctuations given by a Poisson statistics, giving further insight into the properties that we should expect for fluctuating lattice Boltzmann methods.

Integer lattice gas with a sampling collision operator for the fluctuating Navier-Stokes equationThis paper constitutes a step in the direction of developing integer lattice gas methods as an attractive alternative to lattice Boltzmann methods. Here we show that to Boltzmann limit the one-dimensional Blommel integer lattice gas is very close to entropic lattice Boltzmann. More interestingly, the integer lattice gas retains additional correlations that prevent the existence of a well-defined Boltzmann limit. In the analysis of the decaying sine wave we will see that in some situations the bulk viscosity can crucially depend on such correlations beyond the Boltzmann limit. A sampling collision operator, introduced here, can speed up the execution time to make the algorithm obtain comparable computational efficiency to entropic lattice Boltzmann methods.

Molecular Dynamics lattice gas

The basic idea of this research is that a Molecular Dynamics simulation can be mapped onto a lattice gas method by simply following which lattice sites MD particles are assigned to at different times. Interestingly the equilibrium distribution for these discrete occupation numbers closely resemble those of current lattice Boltzmann methods!

Lattice gas with molecular dynamics collision operatorWe introduce a lattice gas implementation that is based on coarse-graining a molecular dynamics (MD) simulation. Such a lattice gas is similar to standard lattice gases, but its collision operator is informed by an underlying MD simulation. This can be considered an optimal lattice gas implementation because it allows for the representation of any system that can be simulated with MD. We show here that equilibrium behavior of the popular lattice Boltzmann algorithm is consistent with this optimal lattice gas. This comparison allows us to make a more accurate identification of the expressions for temperature and pressure in lattice Boltzmann simulations, which turn out to be related not only to the physical temperature and pressure but also to the lattice discretization. We show that for any spatial discretization, we need to choose a particular temporal discretization to recover the lattice Boltzmann equilibrium.

Molecular Dynamics lattice Boltzmann

When taking a Boltzmann limit of a Molecular Dynamics lattice gas one obtains a lattice Boltzmann method.

Molecular dynamics perspectives on nonideal fluid models in the lattice Boltzmann methodLattice Boltzmann models for nonideal fluids rely on mesoscopic force formulations whose connection to microscopic physics remains unclear. By constructing lattice Boltzmann distribution functions directly from molecular dynamics simulations, this work provides a framework for assessing force models against microscopic particle behavior. The analysis shows that a balanced combination of pseudopotential and free-energy formulations best reproduces the moments of the molecularly derived distribution functions, establishing a direct link between microscopic dynamics and mesoscopic fluid modeling.

Ising Model lattice Boltzmann

This ia a new project where we show that it is possible to derive a lattice Boltzmann method that closely resembles an ensemble average of an Ising lattice gas.

Graphical User Interface

Since C doesn't natively has an easy way of generating scientific visualizations, we developed a Graphical User Interface (GUI) that is relatively easy to implement and allows one to control a simulation by changing variable names and by displaying fields and dynamic graphs at runtime. This project is available under the GNU public liscense.

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