Central Moment Lattice Boltzmann Method for Computation of Flows on Stretched Lattice Grids

In order to significantly expand the scope of the lattice Boltzmann (LB) method to more practical applications, particularly in the simulation of complex fluid flows with multiscale flow physics (e.g., wall-bounded flows or mixing layer flows), the use of different grid resolutions in various coordinate directions is essential. This work aims at introducing a central moments-based lattice Boltzmann (LB) scheme using multiple relaxation times (CMRT) for anisotropic meshes. The proposed model is based on a simpler and more stable natural moment basis without using orthogonality and includes additional velocity gradient terms dependent on the grid aspect ratio directly on the post-collision second order central moments to fully restore the required isotropy of the transport coefficients of the normal and shear stresses. The transformation between the distribution functions and various central moments are accomplished via shift matrices. The consistency of CMRT-LB scheme with the Navier-Stokes equations is shown via a Chapman-Enskog expansion. Numerical study for a variety of complex benchmark flow problems demonstrate its accuracy and superior numerical stability at different values of the aspect ratios of the stretched grids, when compared to other existing LB models.