A high-order implicit-explicit flux reconstruction lattice Boltzmann method for viscous incompressible flows

Abstract

In this paper, a high-order implicit-explicit flux reconstruction lattice Boltzmann method (FRLBM) is proposed for simulating viscous incompressible flows. The discrete velocity Boltzmann equation (DVBE) is solved by using a high-order flux reconstruction scheme (FR) for spatial discretization and a high-order implicit-explicit Runge-Kutta scheme (IMEX RK) for time discretization in the generalized curvilinear coordinates with uniform and non-uniform grids to obtain high simulation efficiency. Numerical validations of the proposed method are implemented by simulating (a) Taylor-Green vortex problem, (b) doubly periodic shear layer flow, (c) lid-driven cavity flow, (d) cylindrical Couette flow and (e) flow over a circular cylinder. Numerical results demonstrate that the present method is stable and accurate even at high Reynolds number. Compared with the existing high-order off-lattice Boltzmann methods, the present method is more efficient. In addition, the present method holds the compactness of the standard LBM for parallel computing, but greatly improves the adaptability of complicated geometries.