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Scalable explicit implementation of anisotropic diffusion with Runge-Kutta-Legendre super-time stepping

Vaidya, Bhargav and Prasad, Deovrat and Mignone, Andrea and Sharma, Prateek and Rickler, Luca (2017) Scalable explicit implementation of anisotropic diffusion with Runge-Kutta-Legendre super-time stepping. In: MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 472 (3). pp. 3147-3160.

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Official URL: http://doi.org/10.1093/mnras/stx2176


An important ingredient in numerical modelling of high temperature magnetized astrophysical plasmas is the anisotropic transport of heat along magnetic field lines from higher to lower temperatures. Magnetohydrodynamics typically involves solving the hyperbolic set of conservation equations along with the induction equation. Incorporating anisotropic thermal conduction requires to also treat parabolic terms arising from the diffusion operator. An explicit treatment of parabolic terms will considerably reduce the simulation time step due to its dependence on the square of the grid resolution (Delta x) for stability. Although an implicit scheme relaxes the constraint on stability, it is difficult to distribute efficiently on a parallel architecture. Treating parabolic terms with accelerated super-time-stepping (STS) methods has been discussed in literature, but these methods suffer from poor accuracy (first order in time) and also have difficult-to-choose tuneable stability parameters. In this work, we highlight a second-order (in time) Runge-Kutta-Legendre (RKL) scheme (first described by Meyer, Balsara & Aslam 2012) that is robust, fast and accurate in treating parabolic terms alongside the hyperbolic conversation laws. We demonstrate its superiority over the first-order STS schemes with standard tests and astrophysical applications. We also show that explicit conduction is particularly robust in handling saturated thermal conduction. Parallel scaling of explicit conduction using RKL scheme is demonstrated up to more than 104 processors.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the OXFORD UNIV PRESS, GREAT CLARENDON ST, OXFORD OX2 6DP, ENGLAND
Department/Centre: Division of Physical & Mathematical Sciences > Joint Astronomy Programme
Date Deposited: 03 Nov 2017 10:41
Last Modified: 03 Nov 2017 10:41
URI: http://eprints.iisc.ac.in/id/eprint/58139

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