Mesoscale Methods¶

Mesoscale methods of modelling are capable of tackling larger length and time scales than those available using atomistic methods. By using particles considerably larger than atoms and appropriate choices of interactions between them, these techniques can readily model bulk materials and large structures at the cost of omitting some fine atomic detail. Hydrodynamics start to become more important at these scales: these modelling techniques are thus designed to ensure correct (emergent) fluid behaviour. A mesoscale model can be set up either using a ‘bottom-up’ approach from atomistic models, a ‘top-down’ approach from continuum fluid models, or both.

In this advanced course we will provide an introduction to two mesoscale methods: Dissipative Particle Dynamics (DPD) and the Lattice Boltzmann Equation (LBE) method. We will explain the origins, concepts and algorithms of both methods, as well as their applications, continuing developments and how they can be related to material models at smaller and larger scales (including those covered by the basic lectures).

In the practicals, you will be able to try out DPD and LBE using both simple ‘hackable’ codes and the general-purpose mesoscale modelling package DL_MESO. By the end of the course, you will gain insight into the capabilities of both mesoscale modelling methods. The practicals will consist of a series of guided exercises using the provided codes.

Synopsis¶

Introduction to the Mesoscale¶

Techniques
Physical scales
Mesoscale simulation strategies

Dissipative Particle Dynamics (DPD)¶

DPD algorithm
Fokker-Planck formulation
Application to simple/complex fluids
Boundary conditions
Thermodynamics and DPD
Molecular dynamics and DPD

Lattice Boltzmann Equation (LBE)¶

Classical Boltzmann/Boltzmann Bhatnagar-Gross-Krook (BGK) Equations
Lattice Gas Cellular Automata (LGCA)
Multiple component or “diphasic” LGCA
Lattice Boltzmann Equation method
Lattice Boltzmann BGK Equation and kinetic theory
LBE for multi-component flow