Heidelberg 2022 – wissenschaftliches Programm
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EP: Fachverband Extraterrestrische Physik
EP 6: Astrophysics
EP 6.2: Vortrag
Mittwoch, 23. März 2022, 11:30–11:45, EP-H1
Very high-order subsonic magnetohydrodynamics solvers — •Jean-Mathieu Teissier1 and Wolf-Christian Müller1,2 — 1Technische Universität Berlin, Berlin, Germany — 2Max-Planck/Princeton Center for Plasma Physics, Princeton, NJ, USA
Magnetohydrodynamics (MHD) solvers are very important tools to analyze the large-scale, long time behaviour of astrophysical plasmas. Direct numerical simulations are however linked with high computational costs, so that a trade-off between accuracy of the results and the available resources has to be made. Higher-order solvers, i.e. solvers with a discretization order strictly higher than two, can typically achieve higher accuracy at a lower resolution than second-order ones, leading to an overall gain in performance. However, with increasing discretization order, solvers based on 3D-reconstructions may become prohibitively expensive. We present a finite-volume dimension-by-dimension method which allows to solve for the MHD equations at arbitrarily high discretization orders (we show results up to order ten), while maintaining affordable numerical costs for 3D problems. The magnetic field solenoidality is preserved up to machine precision with the constrained-transport approach. The study is limited to subsonic systems since shocks are not handled properly by higher-order methods. For a discretization order of six and above, the numerical dissipation is too low to prevent a pile-up of energy at small scales in turbulent systems, so that explicit diffusive terms need to be added. We present a formulation to do so, respecting the finite-volume and the constrained-transport frameworks.