Hydrodynamic simulations with the Godunov smoothed particle hydrodynamics
Abstract
We present results based on an implementation of the Godunov smoothed particle hydrodynamics (GSPH), originally developed by Inutsuka, in the GADGET3 hydrodynamic code. We first review the derivation of the GSPH discretization of the equations of moment and energy conservation, starting from the convolution of these equations with the interpolating kernel. The two most important aspects of the numerical implementation of these equations are (a) the appearance of fluid velocity and pressure obtained from the solution of the Riemann problem between each pair of particles, and (b) the absence of an artificial viscosity term. We carry out three different controlled hydrodynamical threedimensional tests, namely the Sod shock tube, the development of KelvinHelmholtz instabilities in a shearflow test and the 'blob' test describing the evolution of a cold cloud moving against a hot wind.
The results of our tests confirm and extend in a number of aspects those recently obtained by Cha, Inutsuka & Nayakshin: (i) GSPH provides a much improved description of contact discontinuities, with respect to smoothed particle hydrodynamics (SPH), thus avoiding the appearance of spurious pressure forces; (ii) GSPH is able to follow the development of gasdynamical instabilities, such as the KevinHelmholtz and the RayleighTaylor ones; (iii) as a result, GSPH describes the development of curl structures in the shearflow test and the dissolution of the cold cloud in the 'blob' test.
Besides comparing the results of GSPH with those from standard SPH implementations, we also discuss in detail the effect on the performances of GSPH of changing different aspects of its implementation: choice of the number of neighbours, accuracy of the interpolation procedure to locate the interface between two fluid elements (particles) for the solution of the Riemann problem, order of the reconstruction for the assignment of variables at the interface, choice of the limiter to prevent oscillations of interpolated quantities in the solution of the Riemann Problem. The results of our tests demonstrate that GSPH is in fact a highly promising hydrodynamic scheme, also to be coupled to an Nbody solver, for astrophysical and cosmological applications.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 October 2011
 DOI:
 10.1111/j.13652966.2011.19021.x
 arXiv:
 arXiv:1105.1344
 Bibcode:
 2011MNRAS.417..136M
 Keywords:

 hydrodynamics;
 instabilities;
 turbulence;
 methods: numerical;
 galaxies: formation;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 19 pages, 13 figures, MNRAS accepted, high resolution version can be obtained at http://adlibitum.oats.inaf.it/borgani/html/papers/gsph_hydrosim.pdf