A Higher Order Pressure Segregation Scheme for the Time-Dependent Magnetohydrodynamics Equations

Institute of Mathematics, Czech Academy of Sciences - Tập 64 - Trang 531-556 - 2019
Yun-Bo Yang1,2, Yao-Lin Jiang1, Qiong-Xiang Kong3
1School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, P.R. China
2Department of Mathematics, Yunnan Normal University, Kunming, Yunnan, P.R. China
3School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, P. R. China

Tóm tắt

A higher order pressure segregation scheme for the time-dependent incompressible magnetohydrodynamics (MHD) equations is presented. This scheme allows us to decouple the MHD system into two sub-problems at each time step. First, a coupled linear elliptic system is solved for the velocity and the magnetic field. And then, a Poisson-Neumann problem is treated for the pressure. The stability is analyzed and the error analysis is accomplished by interpreting this segregated scheme as a higher order time discretization of a perturbed system which approximates the MHD system. The main results are that the convergence for the velocity and the magnetic field are strongly second-order in time while that for the pressure is strongly first-order in time. Some numerical tests are performed to illustrate the theoretical predictions and demonstrate the efficiency of the proposed scheme.

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