Fourth order Galilean invariance for the lattice Boltzmann method. (30th April 2018) - Geier, Martin; Pasquali, Andrea
Highlights: We derive lattice Boltzmann models with fourth order accuracy of the advection. One model uses a body centered cubic lattice. One model uses 33 speeds on a simple cubic lattice. One model uses 27 speeds and a correction using finite differences. The bod centered lattice is found to be stable only for high viscosity. Abstract: Using the structure of a recursive asymptotic analysis we derive conditions on cumulants that guarantee a prescribed order of Galilean invariance for lattice Boltzmann models. We then apply these conditions to three different lattice Boltzmann models and obtain three models with fourth order accurate advection. One of the models uses 27 speeds on a body centered cubic lattice, one uses 33 speeds on an extended Cartesian lattice and one uses 27 speeds plus three finite differences on a Cartesian lattice. All models offer too few degrees of freedom to impose the conditions on the cumulants directly. However, the specific aliasing structure of these lattices permit fourth order accuracy for a model specific optimal reference temperature. Our theoretical derivations are confirmed by measuring the phase lag of traveling vortexes and shear waves.