Equalizing resolution in smoothed-particle hydrodynamics calculations using self-adaptive sinc kernels

¹ Dept. de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Compte d’Urgell 187, 08036 Barcelona, Spain
e-mail: domingo.garcia@upc.edu
² Institut d’Estudis Espacials de Catalunya, Gran Capità 2-4, 08034 Barcelona, Spain
³ Departement Physik, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland

Received: 23 May 2014
Accepted: 18 August 2014

Abstract

Context. The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy, with a resolution that is usually much higher in the compressed regions than in the diluted zones of the fluid.

Aims. We propose and check a method to balance and equalize the resolution of SPH between high- and low-density regions. This method relies on the versatility of a family of interpolators called sinc kernels, which allows increasing the interpolation quality by varying only a single parameter (the exponent of the sinc function).

Methods. The proposed method was checked and validated through a number of numerical tests, from standard one-dimensional Riemann problems in shock tubes, to multidimensional simulations of explosions, hydrodynamic instabilities, and the collapse of a Sun-like polytrope.

Results. The analysis of the hydrodynamical simulations suggests that the scheme devised to equalize the accuracy improves the treatment of the post-shock regions and, in general, of the rarefacted zones of fluids while causing no harm to the growth of hydrodynamic instabilities. The method is robust and easy to implement with a low computational overload. It conserves mass, energy, and momentum and reduces to the standard SPH scheme in regions of the fluid that have smooth density gradients.