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Glimm-Godunov's Method for Cosmic-ray-hydrodynamics

Francesco Miniati
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Abstract

A numerical method for integrating the equations describing a dynamically coupled system made of a fluid and cosmic-rays is developed. In smooth flows the effect of CR pressure is accounted for by modification of the characteristic equations and the energy exchange between cosmic-rays and the fluid, due to diffusive processes in configuration and momentum space, is modeled with a flux conserving method. Provided the shock acceleration efficiency as a function of the upstream conditions and shock Mach number, we show that the Riemann solver can be modified to take into account the cosmic-ray mediation without having to resolve the cosmic-ray induced substructure. Shocks are advanced with Glimm's method which preserves their discontinuous character without any smearing, thus allowing to maintain self-consistency in the shock solutions. In smooth flows either Glimm's or a higher order Godunov's method can be applied, with the latter producing better results when approximations are introduced in the Riemann solver.

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Francesco Miniati. 2007-08-24. Glimm-Godunov's Method for Cosmic-ray-hydrodynamics. https://doi.org/10.1016/j.jcp.2007.08.013

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