Astrophysical fluid simulations of thermally ideal gases with non-constant adiabatic index: numerical implementation
Journal
Date Issued
2015
Author(s)
Description
We would like to thank the referee, Prof. A. Raga, for his constructive suggestions on the paper. B.V. is grateful to the funding support from the University of Torino under the contract: “Progetto di Ateneo-Compagnia di SanPaolo”.
Abstract
Context. An equation of state (EoS) is a relation between thermodynamic state variables and it is essential for closing the set of equations describing a fluid system. Although an ideal EoS with a constant adiabatic index Γ is the preferred choice owing to its simplistic implementation, many astrophysical fluid simulations may benefit from a more sophisticated treatment that can account for diverse chemical processes. Aims: In the present work we first review the basic thermodynamic principles of a gas mixture in terms of its thermal and caloric EoS by including effects like ionization, dissociation, and temperature dependent degrees of freedom such as molecular vibrations and rotations. The formulation is revisited in the context of plasmas that are either in equilibrium conditions (local thermodynamic- or collisional excitation-equilibria) or described by non-equilibrium chemistry coupled to optically thin radiative cooling. We then present a numerical implementation of thermally ideal gases obeying a more general caloric EoS with non-constant adiabatic index in Godunov-type numerical schemes. Methods: We discuss the necessary modifications to the Riemann solver and to the conversion between total energy and pressure (or vice versa) routinely invoked in Godunov-type schemes. We then present two different approaches for computing the EoS. The first employs root-finder methods and it is best suited for EoS in analytical form. The second is based on lookup tables and interpolation and results in a more computationally efficient approach, although care must be taken to ensure thermodynamic consistency. Results: A number of selected benchmarks demonstrate that the employment of a non-ideal EoS can lead to important differences in the solution when the temperature range is 500-104 K where dissociation and ionization occur. The implementation of selected EoS introduces additional computational costs although the employment of lookup table methods (when possible) can significantly reduce the overhead by a factor of ~ 3-4.
Volume
580
Start page
A110
Issn Identifier
0004-6361
Ads BibCode
2015A&A...580A.110V
Rights
open.access
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