Rectangular lattice Boltzmann method using multiple relaxation time collision operator in two and three dimensions

Abstract

We present a lattice Boltzmann (LB) method using a rectangular, non-isotropic lattice based on D2Q9 and D3Q27 velocity sets in two and three dimensions. A second order multi-scale expansion ensures that the scheme correctly reproduces hydrodynamic behaviour. A novel set of basis vectors is introduced in order to allow independent adjustment of eigenvalues corresponding to second order moments as required in order to ensure correct hydrodynamic behaviour using the non-isotropic lattice. Errors are reduced compared to other rectangular grid implementations. Linear perturbation analysis indicates that our scheme has similar stability properties to the isotropic LB method. We investigate the error behaviour of our scheme by performing Taylor-Green vortex flow simulations and comparing our results to simulations using a square grid and also to analytical results. We demonstrate that our scheme is well suited to direct numerical simulation of wall bounded turbulent flows and compare to well known benchmark results.