full
search.png

Search

close.png

Cancel

arrow
Volume 30, Issue 3
Efficient and Stable Schemes for the Magnetohydrodynamic Potential Model

Guo-Dong Zhang & Xiaofeng Yang

DOI: 10.4208/cicp.OA-2020-0113

Commun. Comput. Phys., 30 (2021), pp. 771-798.

Published online: 2021-07

Preview Purchase PDF 2378 39089

Cited by

google scholar semantic scholar
Export citation
  • Abstract

In this paper, we consider the numerical approximations of a magnetohy-drodynamic potential model that was developed in [15]. Several decoupled, linear, unconditionally energy stable schemes are developed by combining some subtle implicit-explicit treatments for nonlinear coupling terms and the projection-type method for the Navier-Stokes equations. The divergence-free condition for the magnetic field is preserved in the fully-discrete level. We further establish the well-posedness and unconditional energy stabilities of the proposed schemes and present a series of numerical examples in 3D, including accuracy/stability tests, benchmark simulations of driven cavity flow and hydromagnetic Kelvin-Helmholtz instability.

  • Keywords

Potential MHD, linear, decoupled, energy stability, second-order, projection method.

  • AMS Subject Headings

65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-30-771, author = {Zhang , Guo-Dong and Yang , Xiaofeng}, title = {Efficient and Stable Schemes for the Magnetohydrodynamic Potential Model}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {3}, pages = {771--798}, abstract = {

In this paper, we consider the numerical approximations of a magnetohy-drodynamic potential model that was developed in [15]. Several decoupled, linear, unconditionally energy stable schemes are developed by combining some subtle implicit-explicit treatments for nonlinear coupling terms and the projection-type method for the Navier-Stokes equations. The divergence-free condition for the magnetic field is preserved in the fully-discrete level. We further establish the well-posedness and unconditional energy stabilities of the proposed schemes and present a series of numerical examples in 3D, including accuracy/stability tests, benchmark simulations of driven cavity flow and hydromagnetic Kelvin-Helmholtz instability.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0113}, url = {http://global-sci.org/intro/article_detail/cicp/19311.html} }
TY - JOUR T1 - Efficient and Stable Schemes for the Magnetohydrodynamic Potential Model AU - Zhang , Guo-Dong AU - Yang , Xiaofeng JO - Communications in Computational Physics VL - 3 SP - 771 EP - 798 PY - 2021 DA - 2021/07 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0113 UR - https://global-sci.org/intro/article_detail/cicp/19311.html KW - Potential MHD, linear, decoupled, energy stability, second-order, projection method. AB -

In this paper, we consider the numerical approximations of a magnetohy-drodynamic potential model that was developed in [15]. Several decoupled, linear, unconditionally energy stable schemes are developed by combining some subtle implicit-explicit treatments for nonlinear coupling terms and the projection-type method for the Navier-Stokes equations. The divergence-free condition for the magnetic field is preserved in the fully-discrete level. We further establish the well-posedness and unconditional energy stabilities of the proposed schemes and present a series of numerical examples in 3D, including accuracy/stability tests, benchmark simulations of driven cavity flow and hydromagnetic Kelvin-Helmholtz instability.

Zhang , Guo-Dong and Yang , Xiaofeng. (2021). Efficient and Stable Schemes for the Magnetohydrodynamic Potential Model. Communications in Computational Physics. 30 (3). 771-798. doi:10.4208/cicp.OA-2020-0113
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard