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Well-balanced schemes for gravitationally stratified media

by R. Käppeli and S. Mishra

(Report number 2014-37)

Abstract
We present a well-balanced scheme for the Euler equations with gravitation. The scheme is capable of maintaining exactly (up to machine precision) a discrete hydrostatic equilibrium without any assumption on a thermodynamic variable such as specific entropy or temperature. The well-balanced scheme is based on a local hydrostatic pressure reconstruction. Moreover, it is computationally efficient and can be incorporated into any existing algorithm in a straightforward manner. The presented scheme improves over standard ones especially when flows close to a hydrostatic equilibrium have to be simulated. The performance of the well-balanced scheme is demonstrated on an astrophysically relevant application: a toy model for core-collapse supernovae.

Keywords: Numerical methods, hydrodynamics, source terms, well-balanced schemes

@Techreport{KM14_587,
  author = {R. K\"appeli and S. Mishra},
  title = {Well-balanced schemes for gravitationally stratified media},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2014-37},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2014/2014-37.pdf },
  year = {2014}
}

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