General equation of state Riemann solvers and their application
Zhuo Chen (University of Alberta)
April 11, 2019
Abstract: Equation of state (EoS) plays an important role in computational (astro-)physics. Solving the hydrodynamic equations together with the equation of state is usually challenging. We propose an efficient Harten-Lax-van Leer-Contact (HLLC) general EoS Riemann solver that could approximately solve the Euler equations and the EoS under the assumption of local thermal equilibrium simultaneously. To justify the new HLLC general EoS Riemann solver, we also develop an exact general EoS Riemann solver that can work with non-convex EoS. By applying Godunov scheme to the new HLLC general EoS Riemann solver, we compare its solutions to the solution of exact Riemann solver and confirm that the approximate solution approaches the exact solution as we increase the resolution. We also confirm that the general EoS Riemann solvers can be reduced to the original EoS Riemann solver if a perfect gas EoS is given to the general EoS Riemann solvers. We propose two methods to solve the EoS, one is to interpolated 2D EoS tables with the bi-linear interpolation method and the other is to calculate the 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. In this research, we use ideal gas that consists of H2, HI, HII, and e- as an example of realistic gas. At last, we apply the HLLC general EoS Riemann solver with analytic EoS solver to the dust-driven asymptotic-giant-branch wind problem in 1D. We find that the light-curve of the AGB star can be significantly different from the one that uses polytropic gas.