A simplified finite volume lattice Boltzmann method for simulations of fluid flows from laminar to turbulent regime, Part I: Numerical framework and its application to laminar flow simulation

In this paper, a finite volume lattice Boltzmann method (FVLBM) based on cell-center unstructured girds is presented and full studied to simulate the incompressible laminar flows, which is simple modified from the cell-vertex unstructured girds FVLBM proposed by Stiebler et al. [Computers & Fluids, 2006, 35(8): 814-819]. Compared with other complex flux reconstruct methods, the computational cost of present scheme is little and can achieve second-order spatial accuracy, the temporal accuracy is adjustable depending on the temporal discretization methods. Different boundary conditions are illustrated and easy implement to the complex geometries. Four cases are testified to validate the present method, including one plate driven Couette flow for accuracy test, flow in the square cavity, flow over the single circular cylinder and more complex double circular cylinders. Numerical experiments show that the present scheme can use relatively few grid cells to simulate relatively higher Reynolds number flow, steady and unsteady flows, demonstrate the good capability of the present method.