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Sapphire++: A Particle Transport Code Combining a Spherical Harmonic Expansion and the Discontinuous Galerkin Method

Sapphire++: a particle transport code combining a spherical harmonic expansion and the discontinuous Galerkin method
Authors: Nils W. Schween; Florian Schulze; Brian Reville;

Sapphire++: A Particle Transport Code Combining a Spherical Harmonic Expansion and the Discontinuous Galerkin Method

Abstract

We present Sapphire++, an open-source code designed to numerically solve the Vlasov-Fokker-Planck equation for astrophysical applications. Sapphire++ employs a numerical algorithm based on a spherical harmonic expansion of the distribution function, expressing the Vlasov-Fokker-Planck equation as a system of partial differential equations governing the evolution of the expansion coefficients. The code utilises the discontinuous Galerkin method in conjunction with implicit and explicit time stepping methods to compute these coefficients, providing significant flexibility in its choice of spatial and temporal accuracy. We showcase the code's validity using examples. In particular, we simulate the acceleration of test particles at a parallel shock and compare the results to analytical predictions. The Sapphire++ code (https://github.com/sapphirepp/sapphirepp) is available as a free and open-source tool for the community.

25 pages, 11 figures, Published in Journal of Computational Physics

Keywords

High Energy Astrophysical Phenomena (astro-ph.HE), particle acceleration, Vlasov-Fokker-Planck, spherical harmonics, FOS: Physical sciences, discontinuous Galerkin method, Physics - Plasma Physics, Plasma Physics (physics.plasm-ph), cosmic rays, numerical methods, Packaged methods for numerical algorithms, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Astrophysics - High Energy Astrophysical Phenomena, Astrophysics - Instrumentation and Methods for Astrophysics, Instrumentation and Methods for Astrophysics (astro-ph.IM), Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Top 10%
Average
Average
Green
hybrid