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, an unstructured grid based finite volume lattice Boltzmann method (FVLBM) that can be used for the simulation of incompressible laminar flows is presented and studied in detail. This method is derived from a simple modification of the cell-vertex unstructured grid based FVLBM proposed by Stiebler et al. (2006). Compared with other complex flux reconstruction methods, the present scheme has a low computational cost and can also achieve second-order spatial accuracy. Furthermore, depending on the use of the different temporal discretization schemes, the temporal accuracy can be adjusted for both steady and unsteady flows. Besides, some comparisons of the computational cost and accuracy with another FVLBM scheme are also presented. Meanwhile, different boundary conditions are illustrated that are easy to implement on complex geometries. To validate the present method, four cases are carried out, including a Couette flow driven by one plate for an accuracy test, flow in a square cavity, flow around a single circular cylinder and a more complex flow around double circular cylinders. Numerical experiments show that the present scheme can simulate steady and unsteady flows at relatively high Reynolds number with relatively few grid cells, thus demonstrating the good capability of the present method.