2D/3D Fully Decoupled, Unconditionally Energy Stable Rotational Velocity Projection Method for Incompressible MHD System

Abstract

The first order linear, fully decoupled rotational velocity projection scheme for settling 2D/3D incompressible magneto-hydrodynamic system is considered in this paper. The considered governing model is a strong nonlinear system and also a double saddle points system. The proposed scheme mainly apply the first order Euler semi implicit scheme for temporal discretization, delicate implicit–explicit treatments for handling the strong nonlinear terms, and the mixed finite element method is used for spatial discretization. Then the system can be transformed into a series of linear elliptic equations such that the all variables are fully decoupled. More importantly, the existence of rotational term in the proposed algorithm makes the theoretical analysis quite difficult to carry out. Therefore, with the help of a Gauge–Uzawa form that we derive the unconditional energy stability. The results of 2D/3D numerical simulations are proved compact with the theoretical analysis.