Improving smoothed particle hydrodynamics with an integral approach to calculating gradients

TL;DR

This paper introduces a tensor-based integral approach to improve gradient calculations in smoothed particle hydrodynamics, enhancing accuracy and conservation in astrophysical simulations.

Contribution

It develops a fully conservative SPH scheme using tensor formulations for derivatives, improving physical magnitude interpolation and applicability to astrophysics.

Findings

Enhanced gradient estimation accuracy.

Improved conservation properties in SPH.

Successful validation with standard tests.

Abstract

In this paper we develop and test a fully conservative SPH scheme based on a tensor formulation that can be applied to simulate astrophysical systems. In the proposed scheme, derivatives are calculated from an integral expression that leads to a tensor (instead of a vectorial) estimation of gradients and reduces to the standard formulation in the continuum limit. The new formulation improves the interpolation of physical magnitudes, leading to a set of conservative equations that resembles those of standard SPH. The resulting scheme is verified using a variety of well-known tests, all of them simulated in two dimensions. We also discuss an application of the proposed tensor method to astrophysics by simulating the stability of a Sun-like polytrope calculated in three dimensions.