A Simple Finite-Volume Formulation of the Lattice Boltzmann Method for Laminar and Turbulent Flows

A finite-volume formulation commonly employed in the well-known SIMPLE family algorithms is used to discretize the lattice Boltzmann equations on a cell-centered, non-uniform grid. The convection terms are treated by a higher-order bounded scheme to ensure accuracy and stability of solutions, especially in the simulation of turbulent flows. The source terms are linearized by a conventional method, and the resulting algebraic equations are solved by a strongly implicit procedure. A method is also presented to link the lattice Boltzmann equations and the macroscopic turbulence modeling equations in the frame of the finite-volume formulation. The method is applied to two different laminar flows and a turbulent flow. The predicted solutions are compared with the experimental data, benchmark solutions, and solutions by the conventional finite-volume method. The results of these numerical experiments for laminar flows show that the present formulation of the lattice Boltzmann method is slightly more diffusive than the finite-volume method when the same numerical grid and convection scheme are used. For a turbulent flow, the finite-volume lattice Boltzmann method slightly underpredicts the reattachment length in a separated flow. In general, the finite-volume lattice Boltzmann method is as accurate as the conventional finite-volume method in predicting the mean velocity and the pressure at the wall. These observations show that the present method is stable and accurate enough to be used in practical simulations of laminar and turbulent flows.