Lattice Boltzmann Methods - Lattices and The DnQm Classification

Lattices and The DnQm Classification

Lattice Boltzmann models can be operated on a number of different lattices, both cubic and triangular, and with or without rest particles in the discrete distribution function.

A popular way of classifying the different methods by lattice is the DnQm scheme. Here "Dn" stands for "n dimensions" while "Qm" stands for "m speeds". For example, D3Q15 is a three-dimensional Lattice Boltzmann model on a cubic grid, with rest particles present. Each node has a crystal shape, and can deliver particles to each of the six neighboring nodes which share a surface, the eight neighboring nodes sharing a corner, and itself. (The D3Q15 model does not contain particles moving to the twelve neighboring nodes which share an edge; adding those would create a "D3Q27" model.)

Real quantities as space and time need to be converted to lattice units prior to simulation. Nondimensional quantities as the Reynolds number remain the same.