The Unsteady Magnetohydrodynamic Equations Of The Gauge Finite Element Method

The unsteady Magnetohydrodynamic(MHD) equation is a coupled and nonlinear model, which describes the law of motion of the conductive fluid in a magnetic field.It is widely used in astrophysics, radar system communication and fluid control. However, this equation has the strong coupling and nonlinear features, which make large-scale computing for the limited computing resources. Therefore, it is necessary to structure a simple and efficient numerical algorithm. This paper is based on the Gauge method to study the two kinds of efficient algorithm for solving the unsteady MHD equations. One is the Gauge-Uzawa finite element algorithm, which is combined with Gauge method and Uzawa method: temporal discretization adopt the first order backward Euler scheme and the second-order backward difference formula(BDF), respectively. The nonlinear term use the semi-implicit scheme and extrapolated scheme, respectively. Spatial discretization adopt the finite element method. Then, we have the first order scheme and the second order scheme for the unsteady MHD equations. Another is the Gauge-Arrow-Hurwicz finite element algorithm, which is based on the idea of the Gauge method and ArrowHurwicz algorithm. Then we give a large number of numerical experiments to validate the stability and effectiveness of these algorithms.