Testing the concept of integral approach to derivatives within the smoothed particle hydrodynamics technique in astrophysical scenarios

TL;DR

This paper evaluates an integral approach to derivatives within the smoothed particle hydrodynamics method, demonstrating improved accuracy, stability, and conservation properties in astrophysical simulations compared to standard SPH.

Contribution

It introduces and validates a fully conservative tensor-based SPH scheme using the integral approach to derivatives, showing enhancements over standard SPH in astrophysical scenarios.

Findings

Better development of hydrodynamic instabilities

Improved description of self-gravitating structures

More stable coalescence simulations of white dwarfs

Abstract

The behavior of IAD_0 scheme, a fully conservative SPH scheme based on a tensor formulation, is analyzed in connection with several astrophysical scenarios, and compared to the same simulations carried out with the standard SPH technique. The proposed hydrodynamic scheme is validated using a variety of numerical tests that cover important topics in astrophysics, such as the evolution of supernova remnants, the stability of self-gravitating bodies and the coalescence of compact objects. The results suggest that the SPH scheme built with the integral approach to the derivatives premise improves the results of the standard SPH technique. In particular, it is observed a better development of hydrodynamic instabilities, an improved description of self-gravitant structures in equilibrium and a reasonable description of the process of coalescence of two white dwarfs. A good energy, and linear and angular momentum conservation, generally better than that of standard SPH, was also obtained. In addition the new scheme is less susceptible to suffer pairing instability.