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We present a new 3D lattice Boltzmann (LB) algorithm based on central momentsfor the D3Q27 lattice using a cuboid grid, which is parameterized by two gridaspect ratios that are related to the ratios of the particle speeds withrespect to that along a reference coordinate direction. The use of the cuboidlattice grid enables the method to compute flows having differentcharacteristic length scales in different directions more efficiently. It isconstructed to simulate the Navier-Stokes equations consistently viaintroducing counteracting corrections to the second order moment equilibriaobtained via a Chapman-Enskog analysis that eliminate the errors associatedwith the grid anisotropy and the non-Galilean invariant terms. Theimplementation is shown to be compact and modular, with an interpretation basedon special matrices, admitting ready extension of the standard algorithm forthe cubic lattice to the cuboid lattice via appropriate scaling of momentsbased on grid aspect ratios before and after collision step and equilibriacorrections. The resulting formulation is general in that the same gridcorrections developed for the D3Q27 lattice for recovering the correct viscousstress tensor is applicable for other lattice subsets, and a variety ofcollision models, including those based on the relaxation of raw moments,central moments and cumulants, as well as their special case involving thedistribution functions. The cuboid central moment LBM is validated against avariety of benchmark flows, and when used in lieu of the corresponding rawmoment formulation for simulating shear flows, we show that it results insignificant improvements in numerical stability. Finally, we demonstrate thatour cuboid LB approach is efficient in simulating anisotropic shear flowproblems with significant savings in computational cost and memory storage whencompared to that based on the cubic lattice.

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows