Higher Order Method Based on the Combination of Local Discontinuous Galerkin and Spectral Deferred Correction Method for the Rotating Navier–Stokes Equations

In this article, the spatial local discontinuous Galerkin (LDG) method and the temporal spectral deferred correction (SDC) method are combined to construct the higher-order approximating method for the unsteady rotating Navier–Stokes equations on the triangular mesh. First, the artificially compressible method is used to circumvent the incompressibility constraint, and the rotating Navier–Stokes equations are transformed into the artificially compressible rotating Navier–Stokes equations. Then, based on equal LDG interpolation and repeated temporal SDC, the higher-order fully discrete method is presented. Theoretically, the stability analysis of the second-order fully discrete method is provided, and it is shown that the time step $\tau$ is stable within the upper bound constraints. Numerical examples are presented to demonstrate the effectiveness of the proposed method.