具有非恒定绝热指数的热理想气体的天体物理流体模拟：数值实现
Astrophysical fluid simulations of thermally ideal gases with non-constant adiabatic index: numerical implementation
摘要：
状态方程（\textit{EoS}）关闭流体方程组。尽管具有恒定\textit{adiabatic index} $Γ$的理想EoS由于其简单的实现而成为优选，但是许多天体物理流体模拟可以受益于可以解释不同化学过程的更复杂的处理。在这里，我们首先审查的基本热力学原理的气体混合物在其热和热量EoS包括电离，解离以及温度依赖的自由度，如分子振动和旋转的影响。该配方是重新审视的等离子体的背景下，无论是在平衡条件下（本地热力学或碰撞激发-平衡）或描述的非平衡化学耦合到光学薄辐射冷却。然后，我们提出了一个数值实现的热理想气体服从一个更一般的热量EoS与非常数绝热指数在Godunov型numerical schemes.We讨论了必要的修改，黎曼求解器和之间的转换，总能量和压力（反之亦然），常规调用Godunov型计划。然后，我们提出了两种不同的方法来计算EoS。第一个采用根查找方法，它是最适合EoS的分析形式。第二个依靠查找表和插值，并在一个更有效的计算方法的结果，但必须小心，以确保热力学的一致性。一些选定的基准表明，就业的非理想的EoS可以导致重要的差异时，温度范围是$500-10^4$ K的解离和电离发生的解决方案。所选EoS的实现引入了额外的计算成本，尽管使用查找表方法可以将开销显著降低$3\sim 4$。
英文摘要：
An Equation of State (\textit{EoS}) closes the set of fluid equations. Although an ideal EoS with a constant \textit{adiabatic index} $Γ$ is the preferred choice due to its simplistic implementation, many astrophysical fluid simulations may benefit from a more sophisticated treatment that can account for diverse chemical processes. Here, 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 as well as 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.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 one employs root-finder methods and it is best suited for EoS in analytical form. The second one leans on lookup table and interpolation and results in a more computationally efficient approach although care must be taken to ensure thermodynamic consistency. 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 $500-10^4$ K where dissociation and ionization occur. The implementation of selected EoS introduces additional computational costs although using lookup table methods can significantly reduce the overhead by a factor $3\sim 4$.
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