On the Piecewise Parabolic Method for Compressible Flow with Stellar Equations of State

TL;DR

This paper evaluates the performance of the piecewise parabolic method in modeling stellar flows with general equations of state, providing direct comparisons and exact solutions for validation.

Contribution

It introduces test problems with exact solutions for stellar equations of state and compares two existing codes' approaches to modeling general gases.

Findings

Different codes show varying accuracy in modeling stellar equations of state.

The provided exact solutions serve as benchmarks for future code validation.

The study highlights the importance of method selection in stellar flow simulations.

Abstract

The piecewise parabolic method and related schemes are widely used to model stellar flows. Several different methods for extending the validity of these methods to a general equation of state have been proposed over time, but direct comparisons amongst one-another and exact solutions with stellar equations of state are not widely available. We introduce some simple test problems with exact solutions run with a popular stellar equation of state and test how two existing codes with different approaches to incorporating general gases perform. The source code for generating the exact solutions is made available.