A projection method for the non-stationary incompressible MHD coupled with the heat equations

Abstract

In this paper, we introduce a linearized projection scheme for non-stationary incompressible coupled the MHD with heat equations, which buoyancy affects because temperature differences in the flow cannot be neglected. The projection algorithm naturally preserves the Gauss’s law and overcomes many shortcomings of previous approaches, which also preserves the electrical field e. Firstly, we establish certain discrete energy estimates based on the projection scheme. Next, we testify the unconditional stability and error estimates of the velocity, pressure, magnetic field and temperature. The regularity of the projection scheme will be given. The numerical results show the method has an optimal convergence order, and can keep Gauss’s law well. The numerical results are consistent with our theoretical analysis, and our method is effective. The numerical method has a good robustness for different cases.