Higher order method based on the coupling of local discontinuous Galerkin method with multistep implicit-explicit time-marching for the micropolar Navier–Stokes equations

In this paper, the spatial local discontinuous Galerkin (LDG) approximation coupled with the temporal multistep implicit-explicit (IMEX) evolution for the micropolar Navier–Stokes equations (MNSE) is adopted to construct an efficient fully discrete method. First, the multistep IMEX-LDG methods are constructed up to the third order, which have small computational scale and facilitate implementation to higher orders. Second, the unconditional stability of the fully discrete method on Cartesian grids is derived theoretically, meaning that the temporal step size τ is upper bounded by a positive constant independent of the spatial mesh size h. Last, numerical results for nonlinear MNSE with different boundary conditions are presented, confirming the theoretical validity and effectiveness of the method.