PT Journal
AU Brynjell-Rahkola, M
TI A spectral element discretization for quasi-static magnetohydrodynamic flows
SO International journal for numerical methods in fluids
JI Int. J. Numer. Methods Fluids
PD July
PY 2024
BP 1795
EP 1812
VL 96
IS 11
PU Wiley
DI 10.1002/fld.5321
WP https://www.db-thueringen.de/receive/dbt_mods_00065902
LA en
DE direct numerical simulation (DNS); liquid metal simulations; magnetohydrodynamics (MHD); Ohm's law; spectral element method (SEM); Strömungsmechanik; Numerisches Verfahren
SN 1097-0363
AB 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.
PI Chichester
ER