Issue |
A&A
Volume 587, March 2016
|
|
---|---|---|
Article Number | A94 | |
Number of page(s) | 16 | |
Section | Numerical methods and codes | |
DOI | https://doi.org/10.1051/0004-6361/201527815 | |
Published online | 23 February 2016 |
A well-balanced finite volume scheme for the Euler equations with gravitation
The exact preservation of hydrostatic equilibrium with arbitrary entropy stratification
Seminar for Applied Mathematics (SAM), Department of
Mathematics,
ETH Zürich,
8092
Zürich,
Switzerland
e-mail:
roger.kaeppeli@sam.math.ethz.ch
Received: 24 November 2015
Accepted: 27 December 2015
Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure gradient is nearly balanced by gravitational forces.
Aims. We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. It therefore can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately.
Methods. A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the well-balanced property is achieved.
Results. The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code that solves time explicitly or implicitly the compressible hydrodynamics equations. We demonstrate the performance of the well-balanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for core-collapse supernovae, convection in carbon shell burning, and a realistic proto-neutron star.
Key words: hydrodynamics / methods: numerical / convection / stars: interiors / stars: neutron
© ESO, 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.