The fully-discrete pseudocompressible methods for micropolar Navier–Stokes equations based on local discontinuous Galerkin and Adams–Bashforth–Moulton methods

In this paper, unified fully-discrete methods for the incompressible micropolar Navier–Stokes equations (MNSE) are considered. Specifically, the pseudocompressible method is introduced to transform the incompressible MNSE into a Cauchy-type problem involving all the original variables. By introducing additional variables, the corresponding equations are rewritten as an equivalent first-order system, and then the ideas of the local discontinuous Galerkin method and the Adams–Bashforth–Moulton method are combined to construct fully-discrete methods up to the third order. Theoretically, the unconditional stability conclusions (the temporal step size τ≤τ0, where τ0 is a positive constant independent of the spatial grid size h) of the fully-discrete methods on rectangular grids are derived. Some numerical results are presented to demonstrate the effectiveness of the proposed methods.