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Implicit hybridized discontinuous Galerkin methods for compressible magnetohydrodynamics
Name
1-s2.0-S2590055219300587-main.pdf
Description
Published version
Size
3.28 MB
Format
Adobe PDF
Checksum (MD5)
f980a103d677641cd0c88bf2cbfe239a
Author(s)
Ciucă, C
Fernandez, P
Christophe, A
Nguyen, NC
Peraire, J
Date Issued
2020
Journal
Journal of Computational Physics: X
Publisher
Elsevier BV
Version
Final published version
Abstract
© 2019 We present hybridized discontinuous Galerkin (HDG) methods for ideal and resistive compressible magnetohydrodynamics (MHD). The HDG methods are fully implicit, high-order accurate and endowed with a unique feature which distinguishes themselves from other discontinuous Galerkin (DG) methods. In particular, they reduce the globally coupled unknowns to the approximate trace of the solution on element boundaries, thereby resulting in considerably smaller global degrees of freedom than other DG methods. Furthermore, we develop a shock capturing method to deal with shocks by appropriately adding artificial bulk viscosity, molecular viscosity, thermal conductivity, and electric resistivity to the physical viscosities in the MHD equations. We show the optimal convergence of the HDG methods for ideal MHD problems and validate our resistive implementation for a magnetic reconnection problem. For smooth problems, we observe that employing a generalized Lagrange multiplier (GLM) formulation can reduce the errors in the divergence of the magnetic field by two orders of magnitude. We demonstrate the robustness of our shock capturing method on a number of test cases and compare our results, both qualitatively and quantitatively, with other MHD solvers. For shock problems, we observe that an effective treatment of both the shock wave and the divergence-free constraint is crucial to ensuring numerical stability.
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Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
10.1016/J.JCPX.2019.100042
