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 - <p style="text-align: justify;">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.</p>