An implicit block LU-SGS finite-volume lattice-Boltzmann scheme for steady flows on arbitrary unstructured meshes

This work proposes a fully implicit lattice Boltzmann (LB) scheme based on finite-volume (FV) discretization on arbitrary unstructured meshes. The linear system derived from the finite-volume lattice Boltzmann equation (LBE) is solved by the block lower-upper (BLU) symmetric-Gauss-Seidel (SGS) algorithm. The proposed implicit FV-LB scheme is efficient and robust, and has a low-storage requirement. The effectiveness and efficiency of the proposed implicit FV-LB scheme are validated and verified by the simulations of three test cases in two dimensions: (a) the laminar Blasius flow over a flat plate with Re=105; (b) the steady viscous flow past a circular cylinder with Re=10, 20, and 40; and (c) the inviscid flow past a circular cylinder. The proposed implicit FV-LB scheme is shown to be not only effective and efficient for simulations of steady viscous flows, but also robust and efficient for simulations of inviscid flows in particular.