An implicit lattice Boltzmann flux solver for simulation of compressible flows

The lattice Boltzmann flux solver (LBFS) is a novel Boltzmann-typed solver under the finite volume framework, which has many advantages over traditional lattice Boltzmann equation (LBE) solvers. However, the existing versions of LBFS are explicit in temporal discretization. Therefore, they are of low computational efficiency and are mostly applied to the simulation of flows around simple geometries. In this paper, an implicit lattice Boltzmann flux solver for compressible flows is proposed, which can efficiently march in time with a large CFL number, and therefore facilitates the simulation of flows around complex geometries in practical engineering applications. Aiming to obtain the time-accurate results of unsteady flows, the implicit LBFS is further combined with the dual time-stepping technique to efficiently simulate unsteady flows, in which a sub-iteration is applied on the pseudo time level. In the sub-iteration, the Jacobian matrix is preconditioned by the lower-upper symmetric Gauss-Seidel (LUSGS) method and solved by the generalized minimal residual method (GMRES). The accuracy and efficiency of the proposed solver are demonstrated by various simulations in a wide Mach number regime. To further demonstrate its performance in practical engineering applications, the proposed solver is also used to simulate the flow over complex aircraft models.