Volume 13, Issue 1
Numerical Analysis and Testing of a Fully Discrete, Decoupled Penalty-Projection Algorithm for MHD in Els?sser Variable

M. Akbas, S. Kaya, M. M. Jaman & L. G. Rebholz

DOI:

Int. J. Numer. Anal. Mod., 13 (2016), pp. 90-113

Published online: 2016-01

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  • Abstract

We consider a fully discrete, effcient algorithm for magnetohydrodynamic (MHD) ow that is based on the Elsässer variable formulation and a timestepping scheme that decouples the MHD system but still provides unconditional stability with respect to the timestep. We prove stability and optimal convergence of the scheme, and also connect the scheme to one based on handling each decoupled system with a penalty-projection method. Numerical experiments are given which verify all predicted convergence rates of our analysis on some analytical test problems, show the results of the scheme on a set of channel flow problems match well the results found when the computation is done with MHD in primitive variable, and finally show the scheme performs well on a channel flow over a step.

  • Keywords

Magnetohydrodynamics Els&#228sser variables Penalty-projection method finite element method

  • AMS Subject Headings

65M60 76W05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-90, author = {M. Akbas, S. Kaya, M. M. Jaman and L. G. Rebholz}, title = {Numerical Analysis and Testing of a Fully Discrete, Decoupled Penalty-Projection Algorithm for MHD in Els?sser Variable}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {1}, pages = {90--113}, abstract = {We consider a fully discrete, effcient algorithm for magnetohydrodynamic (MHD) ow that is based on the Elsässer variable formulation and a timestepping scheme that decouples the MHD system but still provides unconditional stability with respect to the timestep. We prove stability and optimal convergence of the scheme, and also connect the scheme to one based on handling each decoupled system with a penalty-projection method. Numerical experiments are given which verify all predicted convergence rates of our analysis on some analytical test problems, show the results of the scheme on a set of channel flow problems match well the results found when the computation is done with MHD in primitive variable, and finally show the scheme performs well on a channel flow over a step.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/428.html} }
TY - JOUR T1 - Numerical Analysis and Testing of a Fully Discrete, Decoupled Penalty-Projection Algorithm for MHD in Els?sser Variable AU - M. Akbas, S. Kaya, M. M. Jaman & L. G. Rebholz JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 90 EP - 113 PY - 2016 DA - 2016/01 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/428.html KW - Magnetohydrodynamics KW - Elsässer variables KW - Penalty-projection method KW - finite element method AB - We consider a fully discrete, effcient algorithm for magnetohydrodynamic (MHD) ow that is based on the Elsässer variable formulation and a timestepping scheme that decouples the MHD system but still provides unconditional stability with respect to the timestep. We prove stability and optimal convergence of the scheme, and also connect the scheme to one based on handling each decoupled system with a penalty-projection method. Numerical experiments are given which verify all predicted convergence rates of our analysis on some analytical test problems, show the results of the scheme on a set of channel flow problems match well the results found when the computation is done with MHD in primitive variable, and finally show the scheme performs well on a channel flow over a step.
M. Akbas, S. Kaya, M. M. Jaman & L. G. Rebholz. (1970). Numerical Analysis and Testing of a Fully Discrete, Decoupled Penalty-Projection Algorithm for MHD in Els?sser Variable. International Journal of Numerical Analysis and Modeling. 13 (1). 90-113. doi:
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