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A type of overlapping grid in spherical coordinates called the Yin-Yang gridis successfully implemented into a 3D version of the explicit Euleriangrid-based code PROMETHEUS including self-gravity. The modified codesuccessfully passed several standard hydrodynamic tests producing results whichare in very good agreement with analytic solutions. Moreover, the solutionsobtained with the Yin-Yang grid exhibit no peculiar behaviour at the boundarybetween the two grid patches. The code has also been successfully used to modelastrophysically relevant situations, namely equilibrium polytropes, aTaylor-Sedov explosion, and Rayleigh-Taylor instabilities. According to ourresults, the usage of the Yin-Yang grid greatly enhances the suitability andefficiency of 3D explicit Eulerian codes based on spherical polar coordinatesfor astrophysical flows.

An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows