A spectral element discretization for quasi-static magnetohydrodynamic flows Brynjell-Rahkola, Mattias article article article Text https://doi.org/10.1002/fld.5321 https://www.db-thueringen.de/receive/dbt_mods_00065902 http://uri.gbv.de/document/gvk:ppn:189236946X doc-type:Article ScholarlyArticle ddc:510 direct numerical simulation (DNS) -- liquid metal simulations -- magnetohydrodynamics (MHD) -- Ohm's law -- spectral element method (SEM) The classical staggered PN-PN-2 spectral element method (SEM) is revisited and extended to quasi-static magnetohydrodynamic (MHD) flows. In this realm, which is valid in the limit of vanishing magnetic Reynolds number, the evaluation of the Lorentz force in the momentum equation requires the electric current density, governed by Ohm's law and a charge conservation condition derived from Ampère's law, to be determined. Once discretized with the SEM, this translates into solving one additional problem for the electric potential involving the so-called consistent Poisson operator. The method is well suited for fully three-dimensional flows in complex geometries. Changes in resolution requirements aside, consideration of the electromagnetic quantities is estimated to increase the computational cost associated with MHD by about 40% relative to hydrodynamics. The accuracy and the capabilities of the scheme is demonstrated on a set of common flows from the MHD literature. Exponential convergence with polynomial order is confirmed for the electric current density. 2024-07-19 Wiley 18 Seiten eng International journal for numerical methods in fluids -- Int. J. Numer. Methods Fluids -- Internat J Numer Methods Fluids -- Int. J. Numer. Meth. Fluids -- http://uri.gbv.de/document/gvk:ppn:302466762 -- 1097-0363 -- 1491176-0 public https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess