Well-Balanced Hydrodynamics for the Piecewise Parabolic Method with Characteristic Tracing

TL;DR

This paper introduces a well-balanced reconstruction technique adapted for the piecewise parabolic method in hydrodynamics, ensuring hydrostatic equilibrium is maintained during simulations, with a provided Python implementation.

Contribution

It presents a novel adaptation of well-balanced methods to the PPM hydrodynamics scheme, enhancing stability and accuracy in stellar hydrodynamics simulations.

Findings

Maintains hydrostatic equilibrium during simulations

Provides a Python implementation of the method

Improves stability and accuracy in stellar hydrodynamics

Abstract

Well-balanced reconstruction techniques have been developed for stellar hydrodynamics to address the challenges of maintaining hydrostatic equilibrium during evolution. I show how to adapt a simple well-balanced method to the piecewise parabolic method for hydrodynamics. A python implementation of the method is provided.