A Grad-Div Stabilization and Rotational Pressure-Correction Method for the Unsteady Incompressible Thermosolutal Convection Coupled with Magnetohydrodynamic System

Abstract

In this paper, we propose a grad-div stabilization and rotational pressure-correction (GSRP) method with second-order temporal discretization for solving the unsteady incompressible thermosolutal convection coupled with magnetohydrodynamics (UITC-MHD) system. The method simultaneously enhances computational accuracy and improves discrete mass conservation in time-discrete numerical simulations. We rigorously establish stability and derive error estimates for time-discrete solutions in the $L^2$- and $H^1$-norms. Notably, the pressure converges with an order of 1.5 in the $L^2$-norm, aligning with theoretical predictions [1]. Finally, the convergence and robustness of the GSRP method are confirmed through a series of numerical experiments conducted in both 2D and 3D.