Abstract
This article provides a concise exposition of the multiple–relaxation–time lattice Boltzmann equation, with examples of 15–velocity and 19–velocity models in three dimensions. Simulation of a diagonally lid–driven cavity flow in three dimensions at Re = 500 and 2000 is performed. The results clearly demonstrate the superior numerical stability of the multiple–relaxation–time lattice Boltzmann equation over the popular lattice Bhatnagar–Gross–Krook equation.