Local discontinuous Galerkin method coupled with the implicit-explicit Runge–Kutta method for the time-dependent micropolar fluid equations

Abstract

In this article, the spatial local discontinuous Galerkin (LDG) approximation coupled with the temporal implicit-explicit Runge–Kutta (RK) evolution for the micropolar fluid equations are adopted to construct the discretization method. To avoid the incompressibility constraint, the artificial compressibility strategy method is used to convert the micropolar fluid equations into the Cauchy–Kovalevskaja type equations. Then the LDG method based on the modal expansion and the implicit-explicit RK method are properly combined to construct the expected third-order method. Theoretically, the unconditionally stable of the fully discrete method are derived in multidimensions for triangular meshs. And the numerical experiments are given to verify the theoretical and effectiveness of the presented methods.