Three-Dimensional Lattice Boltzmann Flux Solver and Its Applications to Incompressible Isothermal and Thermal Flows (Communications in Computational Physics, 2018)
A three-dimensional (3D) lattice Boltzmann flux solver (LBFS) is presentedin this paper for the simulation of both isothermal and thermal flows. The presentsolver combines the advantages of conventional Navier-Stokes (N-S) solvers and latticeBoltzmann equation (LBE) solvers. It applies the finite volume method (FVM) tosolve the N-S equations. Different from the conventional N-S solvers, its viscous andinviscid fluxes at the cell interface are evaluated simultaneously by local reconstructionof LBE solution. As compared to the conventional LBE solvers, which apply thelattice Boltzmann method (LBM) globally in the whole computational domain, it onlyapplies LBM locally at each cell interface, and flow variables at cell centers are givenfrom the solution of N-S equations. Since LBM is only applied locally in the 3D LBFS,the drawbacks of the conventional LBM, such as limitation to uniform mesh, tie-upof mesh spacing and time step, tedious implementation of boundary conditions, arecompletely removed. The accuracy, efficiency and stability of the proposed solver areexamined in detail by simulating plane Poiseuille flow, lid-driven cavity flow and naturalconvection. Numerical results show that the LBFS has a second order of accuracyin space. The efficiency of the LBFS is lower than LBM on the same grids. However,the LBFS needs very less non-uniform grids to get grid-independence results and itsefficiency can be greatly improved and even much higher than LBM. In addition, theLBFS is more stable and robust.