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A well-balanced scheme for the Euler equations with gravitation

by R. Käppeli

(Report number 2016-53)

Abstract
We present a novel well-balanced scheme for the Euler equations with gravitation. The scheme is designed to preserve exactly an isothermal hydrostatic equilibrium. It uses a novel equilibrium preserving reconstruction based on the Gibbs free energy. Moreover, the developed scheme is applicable beyond the ideal gas law which is crucial for many astrophysical applications. The scheme is second-order accurate in space and can easily be implemented into any existing code solving time explicitly or implicitly the Euler equations. We assess the performance of the scheme on two test problems involving a realistic equation of state for stellar matter.

Keywords: Numerical methods, Hydrodynamics, Source terms, Well-balanced schemes

@Techreport{K16_690,
  author = {R. K\"appeli},
  title = {A well-balanced scheme for the Euler equations with gravitation},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2016-53},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2016/2016-53.pdf },
  year = {2016}
}

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