A grad‐div stabilized method using the Jacobi iteration for the thermally coupled incompressible magnetohydrodynamic system

Abstract

AbstractThis paper presents a grad‐div stabilization with the Jacobi iteration to the thermally coupled incompressible magnetohydrodynamic system, which avoids breakdown of solver and increase of computational time with increasing value of grad‐div stabilized parameter. The proposed method includes two steps: a fully discrete first‐order Euler semi‐implicit scheme based on the mixed finite element method is implemented for the considered problem in Step 1. Then, in Step 2, the Jacobi approximation is applied to the grad‐div operator whose each component will be decoupled. Moreover, we obtain theoretical analysis results of the presented method, both unconditional stability and convergence analysis. Finally, some numerical experiments are presented to show the accuracy and verify effectiveness of the proposed method.