A higher order pressure segregation scheme for the time-dependent magnetohydrodynamics equations

Yun-Bo Yang; Yao-Lin Jiang; Qiong-Xiang Kong

Applications of Mathematics (2019)

  • Volume: 64, Issue: 5, page 531-556
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Yang, Yun-Bo, Jiang, Yao-Lin, and Kong, Qiong-Xiang. "A higher order pressure segregation scheme for the time-dependent magnetohydrodynamics equations." Applications of Mathematics 64.5 (2019): 531-556. <http://eudml.org/doc/294421>.

@article{Yang2019,
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.},
author = {Yang, Yun-Bo, Jiang, Yao-Lin, Kong, Qiong-Xiang},
journal = {Applications of Mathematics},
keywords = {magnetohydrodynamics equations; pressure segregation method; higher order scheme; stability; error estimate},
language = {eng},
number = {5},
pages = {531-556},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A higher order pressure segregation scheme for the time-dependent magnetohydrodynamics equations},
url = {http://eudml.org/doc/294421},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Yang, Yun-Bo
AU - Jiang, Yao-Lin
AU - Kong, Qiong-Xiang
TI - A higher order pressure segregation scheme for the time-dependent magnetohydrodynamics equations
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 5
SP - 531
EP - 556
AB - 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.
LA - eng
KW - magnetohydrodynamics equations; pressure segregation method; higher order scheme; stability; error estimate
UR - http://eudml.org/doc/294421
ER -

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