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  High-order magnetohydrodynamics for astrophysics with an adaptive mesh refinement discontinuous Galerkin scheme

Guillet, T., Pakmor, R., Springel, V., Chandrashekar, P., & Klingenberg, C. (2019). High-order magnetohydrodynamics for astrophysics with an adaptive mesh refinement discontinuous Galerkin scheme. Monthly Notices of the Royal Astronomical Society, 485(3), 4209-4246. doi:10.1093/mnras/stz314.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0004-71EB-4 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-71EC-3
Genre: Journal Article

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Guillet, Thomas, Author
Pakmor, Rüdiger1, Author              
Springel, Volker2, Author              
Chandrashekar, Praveen, Author
Klingenberg, Christian, Author
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1Stellar Astrophysics, MPI for Astrophysics, Max Planck Society, ou_159882              
2Computational Structure Formation, MPI for Astrophysics, Max Planck Society, ou_2205642              

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 Abstract: Modern astrophysical simulations aim to accurately model an ever-growing array of physical processes, including the interaction of fluids with magnetic fields, under increasingly stringent performance and scalability requirements driven by present-day trends in computing architectures. Discontinuous Galerkin (DG) methods have recently gained some traction in astrophysics, because of their arbitrarily high order and controllable numerical diffusion, combined with attractive characteristics for high-performance computing. In this paper, we describe and test our implementation of a DG scheme for ideal magnetohydrodynamics (MHD) in the arepo-dg code. Our DG-MHD scheme relies on a modal expansion of the solution on Legendre polynomials inside the cells of an Eulerian octree-based adaptive mesh refinement grid. The divergence-free constraint of the magnetic field is enforced using one out of two distinct cell-centred schemes: either a Powell-type scheme based on non-conservative source terms, or a hyperbolic divergence cleaning method. The Powell scheme relies on a basis of locally divergence-free vector polynomials inside each cell to represent the magnetic field. Limiting prescriptions are implemented to ensure non-oscillatory and positive solutions. We show that the resulting scheme is accurate and robust: it can achieve high-order and low numerical diffusion, as well as accurately capture strong MHD shocks. In addition, we show that our scheme exhibits a number of attractive properties for astrophysical simulations, such as lower advection errors and better Galilean invariance at reduced resolution, together with more accurate capturing of barely resolved flow features. We discuss the prospects of our implementation, and DG methods in general, for scalable astrophysical simulations.

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 Dates: 2019-01-30
 Publication Status: Published online
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 Rev. Method: Peer
 Identifiers: DOI: 10.1093/mnras/stz314
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Title: Monthly Notices of the Royal Astronomical Society
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Source Genre: Journal
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Publ. Info: OXFORD : OXFORD UNIV PRESS
Pages: - Volume / Issue: 485 (3) Sequence Number: - Start / End Page: 4209 - 4246 Identifier: ISSN: 0035-8711
CoNE: https://pure.mpg.de/cone/journals/resource/1000000000021470