Central moment lattice Boltzmann method on a rectangular lattice

Simulating inhomogeneous flows with different characteristic scales in coordinate directions using the collide-and-stream based lattice Boltzmann methods (LBM) can be accomplished efficiently rectangular grids. We develop and investigate a new central moment LBM on non-orthogonal basis (referred to as RC-LBM). The equilibria which moments relax under collision this approach are obtained from matching those corresponding continuous Maxwell distribution. A Chapman-Enskog analysis is performed derive correction terms second order involving grid aspect ratio velocity gradients that restores isotropy of viscous stress tensor eliminates non-Galilean invariant cubic resulting hydrodynamical equations. special case formulation raw RNR-LBM) also constructed. schemes represent considerable simplification, especially for transformation matrices corrections, improvement over existing MRT-LB grids use orthogonal basis. Numerical validation study both RC-LBM RNR-LBM variety benchmark flow problems show good accuracy at various ratios. ability our proposed simulate relatively lower ratios than considered prior LB approaches demonstrated. Furthermore, simulations reveal superior stability characteristics handling shear viscosities and/or higher velocities. In addition, computational advantages lieu square shown.