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

Abstract

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. In this work, we propose and check a scheme 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). The scheme is 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. The analysis of the hydrodynamical simulations suggests that the scheme devised to equalizing 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.

29 pages, 18 figures, accepted by A&A

References in corpus (8)

• SPLASH: An interactive visualisation tool for Smoothed Particle Hydrodynamics simulations
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• Smoothed Particle Hydrodynamics and Magnetohydrodynamics
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• Astrophysical Smooth Particle Hydrodynamics
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Cited by in corpus (7)

• Numerical Convergence in Smoothed Particle Hydrodynamics
• An advanced leakage scheme for neutrino treatment in astrophysical simulations
• SPHYNX: an accurate density-based SPH method for astrophysical applications
• Improved Performances in Subsonic Flows of an SPH Scheme with Gradients Estimated using an Integral Approach
• Parallel adaptive weakly-compressible SPH for complex moving geometries
• Mixing Sinc kernels to improve interpolations in smoothed particle hydrodynamics without pairing instability
• Optimized smoothing kernels for SPH