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Applications of Mathematics

, Volume 64, Issue 5, pp 531–556 | Cite as

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

  • Yun-Bo Yang
  • Yao-Lin Jiang
  • Qiong-Xiang KongEmail author
Article
  • 28 Downloads

Abstract

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.

Keywords

magnetohydrodynamics equations pressure segregation method higher order scheme stability error estimate 

MSC 2010

65N15 65N30 65N12 

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Copyright information

© Mathematical Institute, Academy of Sciences of Cz 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’an, ShaanxiP. R. China
  2. 2.Department of MathematicsYunnan Normal UniversityKunming, YunnanP. R. China
  3. 3.School of Human Settlements and Civil EngineeringXi’an Jiaotong UniversityXi’an, ShaanxiP. R. China

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