Issue |
A&A
Volume 514, May 2010
|
|
---|---|---|
Article Number | A48 | |
Number of page(s) | 14 | |
Section | Numerical methods and codes | |
DOI | https://doi.org/10.1051/0004-6361/200913435 | |
Published online | 12 May 2010 |
An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows
Max-Planck Institut für Astrophysik,
Karl-Schwarzschild-Straße 1, 85740 Garching, Germany e-mail: emueller@mpa-garching.mpg.de
Received:
9
October
2009
Accepted:
3
March
2010
Aims. Three dimensional explicit hydrodynamic codes based on spherical polar coordinates using a single spherical polar grid suffer from a severe restriction of the time step size due to the convergence of grid lines near the poles of the coordinate system. More importantly, numerical artifacts are encountered at the symmetry axis of the grid where boundary conditions have to be imposed that flaw the flow near the axis. The first problem can be eased and the second one avoided by applying an overlapping grid technique.
Methods. A type of overlapping grid in spherical coordinates is adopted. This
so called “Yin-Yang” grid is a two-patch overset grid proposed by
Kageyama and Sato for geophysical simulations. Its two grid patches
contain only the low-latitude regions of the usual spherical polar
grid and are combined together in a simple manner. This property of
the Yin-Yang grid greatly simplifies its implementation into a 3D code
already employing spherical polar coordinates. It further allows for a
much larger time step in 3D simulations using high angular resolution
(1°) than that required in 3D simulations using a regular
spherical grid with the same angular resolution.
Results. The Yin-Yang grid is successfully implemented into a 3D version of the explicit Eulerian grid-based code PROMETHEUS including self-gravity. The modified code successfully passed several standard hydrodynamic tests producing results which are in very good agreement with analytic solutions. Moreover, the solutions obtained with the Yin-Yang grid exhibit no peculiar behaviour at the boundary between the two grid patches. The code has also been successfully used to model astrophysically relevant situations, namely equilibrium polytropes, a Taylor-Sedov explosion, and Rayleigh-Taylor instabilities. According to our results, the usage of the Yin-Yang grid greatly enhances the suitability and efficiency of 3D explicit Eulerian codes based on spherical polar coordinates for astrophysical flows.
Key words: methods: numerical / hydrodynamics / gravitation / supernovae: general
© ESO, 2010
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