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

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

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

Published online: 2016-01

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  • Abstract

We consider a fully discrete, efficient algorithm for magnetohydrodynamic (MHD) flow 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, Elsässer 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 = {Akbas , M.Kaya , S.Mohebujjaman , M. and Rebholz , L. G.}, title = {Numerical Analysis and Testing of a Fully Discrete, Decoupled Penalty-Projection Algorithm for MHD in Elsässer Variable}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {1}, pages = {90--113}, abstract = {

We consider a fully discrete, efficient algorithm for magnetohydrodynamic (MHD) flow 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 Elsässer Variable AU - Akbas , M. AU - Kaya , S. AU - Mohebujjaman , M. AU - Rebholz , L. G. 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, Elsässer variables, Penalty-projection method, finite element method. AB -

We consider a fully discrete, efficient algorithm for magnetohydrodynamic (MHD) flow 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.

Akbas , M.Kaya , S.Mohebujjaman , M. and Rebholz , L. G.. (2016). Numerical Analysis and Testing of a Fully Discrete, Decoupled Penalty-Projection Algorithm for MHD in Elsässer Variable. International Journal of Numerical Analysis and Modeling. 13 (1). 90-113. doi:
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