TY - JOUR
T1 - A fourth-order accurate finite volume method for ideal MHD via upwind constrained transport
AU - Felker, Kyle Gerard
AU - Stone, James McLellan
N1 - Funding Information:
The authors thank Thomas Gardiner for discussion and comments on an early draft of this manuscript. K.G.F. was supported by the Department of Energy Computational Science Graduate Fellowship (CSGF), grant number DE-FG02-97ER25308 . J.M.S. was supported by National Science Foundation , grant number AST-1715277 .
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2018/12/15
Y1 - 2018/12/15
N2 - We present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation laws with the upwind constrained transport (UCT) framework to ensure that the divergence-free constraint of the magnetic field is satisfied. A novel implementation of UCT that uses the piecewise parabolic method (PPM) for the reconstruction of magnetic fields at cell corners in 2D is introduced. The resulting scheme can be expressed as the extension of the second-order accurate constrained transport (CT) Godunov-type scheme that is currently used in the Athena astrophysics code. After validating the base algorithm on a series of hydrodynamics test problems, we present the results of multidimensional MHD test problems which demonstrate formal fourth-order convergence for smooth problems, robustness for discontinuous problems, and improved accuracy relative to the second-order scheme.
AB - We present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation laws with the upwind constrained transport (UCT) framework to ensure that the divergence-free constraint of the magnetic field is satisfied. A novel implementation of UCT that uses the piecewise parabolic method (PPM) for the reconstruction of magnetic fields at cell corners in 2D is introduced. The resulting scheme can be expressed as the extension of the second-order accurate constrained transport (CT) Godunov-type scheme that is currently used in the Athena astrophysics code. After validating the base algorithm on a series of hydrodynamics test problems, we present the results of multidimensional MHD test problems which demonstrate formal fourth-order convergence for smooth problems, robustness for discontinuous problems, and improved accuracy relative to the second-order scheme.
KW - Constrained transport
KW - High-order finite volume method
KW - Magnetohydrodynamics
KW - Numerical methods
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U2 - 10.1016/j.jcp.2018.08.025
DO - 10.1016/j.jcp.2018.08.025
M3 - Article
AN - SCOPUS:85054384810
SN - 0021-9991
VL - 375
SP - 1365
EP - 1400
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -