Mesoscale Methods

The mesoscale course at the summer school covers two frequently used mesoscale modelling techniques: Dissipative Particle Dynamics (DPD) and the Lattice Boltzmann (LB) method. Background information is initially provided on why mesoscale methods are necessary, their possible areas of application and how they can be approached 'bottom-up' or 'top-down'. 

DPD is then presented, giving the method's origins and details of the algorithm (including how it satisfies Fokker-Planck fluctuation theory), as well as how it can be applied to complex fluid systems, how boundaries can be defined for the method, how the correct thermodynamics can be achieved and how DPD can be obtained by coarse-graining atomistic molecular dynamics.

The LB method is presented, starting with its theoretical background and demonstrating how LB can be obtained either from Lattice Gas Cellular Automata (LGCA) or kinetic theory via Boltzmann's equation. By applying the simple but frequently used Bhatnagar-Gross-Krook algorithm for particle collisions, the connection between LB and the Navier-Stokes equations for fluid flows using Chapman-Enskog expansion is demonstrated. The features of the LB method are shown to allow simple boundary conditions for systems with complex geometries as well as multicomponent (multiple fluid or phase) flows.

Practical computing exercises for both DPD and LB are provided to give students the opportunity to try out both methods and gain an understanding of their possibilities.


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