Solving the Riemann problem for realistic astrophysical fluids

Abstract

We present new methods to solve the Riemann problem both exactly and approximately for general equations of state (EoS) to facilitate realistic modeling and understanding of astrophysical flows. The existence and uniqueness of the new exact general EoS Riemann solution can be guaranteed if the EoS is monotone regardless of the physical validity of the EoS. We confirm that: (1) the solution of the new exact general EoS Riemann solver and the solution of the original exact Riemann solver match when calculating perfect gas Euler equations; (2) the solution of the new Harten-Lax-van Leer-Contact (HLLC) general EoS Riemann solver and the solution of the original HLLC Riemann solver match when working with perfect gas EoS; and (3) the solution of the new HLLC general EoS Riemann solverapproaches the new exact solution. We solve the EoS with two methods, one is to interpolate 2D EoS tables by the bi-linear interpolation method, and the other is to analytically calculate thermodynamic variables at run-time. The interpolation method is more general as it can work with other monotone and realistic EoS, while the analytic EoS solver introduced here works with a relatively idealized EoS. Numerical results confirm that the accuracy of the two EoS solvers is similar. We study the efficiency of these two methods with the HLLC general EoS Riemann solver and find that analytic EoS solver is faster in the test problems. However, we point out that a combination of the two EoS solvers may become favorable in some specific problems. Throughout this research, we assume local thermal equilibrium.

A 3D Radiation Hydrodynamic AGB Binary Model

“…We take into account dust which can be destroyed by shocks, a high temperature close to an LTE environment, and if radiation from the AGB star can sublimate the small dust grains (see Section 3.2 for detail). We calculate the cooling strength on H 2 , H, and H + ; their number densities are found by solving the Saha equation (Chen et al 2019). We model the AGB star as an inner boundary condition that has sinusoidally varying radial velocity (Bowen 1988).…”

“…The ratios we adopted in our simulations make sense only for some oxygen-rich AGB stars. We calculate n H + , n H , and n H2 by solving the thermal equilibrium problem, i.e., the Saha equation with the local ρ and T (Chen et al 2019)…”

“…In AGB stars' atmosphere, the internal energy change in phase transitions, e.g. H 2 H and H H + + e − is significant compared to the kinetic part of thermal energy (Chen et al 2019) and radiation energy. Freytag & Höfner (2008) used a Roe-type Riemann solver with a tabulated equation of state to resolve the ionization.…”

Planetary Accretion Shocks with a Realistic Equation of State

“…As a first study, we incorporate such physics but make a simplified assumption of chemical localthermal equilibrium (LTE) of H 2 , H, and H + . The abundance of these species can be obtained analytically from the Saha equations at runtime according to Appendix C of Chen et al (2019). The EoS is given by = (ρ, T g ) in an analytical from, which avoids the use of a tabulated EoS and improves the efficiency and accuracy in our simulations.…”

The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers

“…A complete description of the implementation of the general EOS functionality in Athena++ is provided in Coleman (2019). This functionality is validated using tests from Chen et al (2019).…”