Finite Volume Lattice Boltzmann Method for Nearly Incompressible Flows on Arbitrary Unstructured Meshes (Communications in Computational Physics, 2018)
A genuine finite volume method based on the lattice Boltzmann equation(LBE) for nearly incompressible flows is developed. The proposed finite volume latticeBoltzmann method (FV-LBM) is grid-transparent, i.e., it requires no knowledge ofcell topology, thus it can be implemented on arbitrary unstructured meshes for effectiveand efficient treatment of complex geometries. Due to the linear advection term inthe LBE, it is easy to construct multi-dimensional schemes. In addition, inviscid andviscous fluxes are computed in one step in the LBE, as opposed to in two separate stepsfor the traditional finite-volume discretization of the Navier-Stokes equations. Becauseof its conservation constraints, the collision term of the kinetic equation can be treatedimplicitly without linearization or any other approximation, thus the computationalefficiency is enhanced. The collision with multiple-relaxation-time (MRT) model isused in the LBE. The developed FV-LBM is of second-order convergence. The proposedFV-LBM is validated with three test cases in two-dimensions: (a) the Poiseuilleflow driven by a constant body force; (b) the Blasius boundary layer; and (c) the steadyflow past a cylinder at the Reynolds numbers Re=10, 20, and 40. The results verify thedesigned accuracy and efficacy of the proposed FV-LBM.