Note on the usage of grad-div stabilization for the penalty-projection algorithm in magnetohydrodynamics
Document Type
Article
Publication Date
5-15-2019
Abstract
© 2018 Elsevier Inc. An algorithm for resolving magnetohydrodynamic (MHD) flows has been presented recently, that allows for a stable decoupling of the system and uses the penalty-projection method for extra efficiency. The algorithm relies on the choice of Scott–Vogelius finite elements to complement the grad-div stabilization. We propose a small modification of the algorithm, which allows for its usage even with the less sophisticated (and more computationally attractive) Taylor-Hood pair of finite element spaces. We demonstrate numerically, that the new modification of the method is first order accurate in time (as expected by the theory), while the existing method would fail on the Taylor–Hood finite elements (the blow-up of the solution is demonstrated).
Publication Title
Applied Mathematics and Computation
Recommended Citation
Erkmen, D.,
&
Labovsky, A.
(2019).
Note on the usage of grad-div stabilization for the penalty-projection algorithm in magnetohydrodynamics.
Applied Mathematics and Computation,
349, 97-101.
http://doi.org/10.1016/j.amc.2018.12.028
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5916