A gas-kinetic BGK scheme for the finite volume lattice Boltzmann method for nearly incompressible flows

•A gas kinetic BGK scheme based finite volume lattice Boltzmann method is proposed.•The proposed method achieves second order accuracy of time and space in one step.•For the steady state, the present scheme becomes the exact central-difference scheme.•The proposed scheme is a reliable and accurate tool for incompressible flows.•The proposed scheme works on arbitrary meshes.