Numerical Analysis and Testing of a Fully Discrete, Decoupled Penalty-Projection Algorithm for MHD in Elsässer Variable
Year: 2016
Author: M. Akbas, S. Kaya, M. Mohebujjaman, L. G. Rebholz
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-428
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 90–113
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Magnetohydrodynamics Elsässer variables Penalty-projection method finite element method.