A one-parameter family of interpolating kernels for Smoothed Particle Hydrodynamics studies

TL;DR

This paper introduces a family of interpolating kernels for Smoothed Particle Hydrodynamics that are flexible and adaptable, improving the tracking of discontinuities like shock fronts by varying a single parameter.

Contribution

It presents a new one-parameter family of kernels for SPH that can be tuned for different simulation needs, bridging standard and more condensed kernels.

Findings

For n=3, similar to the cubic-spline kernel.

For n>3, kernels are more centrally condensed.

Enhanced ability to track discontinuities.

Abstract

A set of interpolating functions of the type f(v)={(sin[v pi/2])/(v pi/2)}^n is analyzed in the context of the smoothed-particle hydrodynamics (SPH) technique. The behaviour of these kernels for several values of the parameter n has been studied either analytically as well as numerically in connection with several tests carried out in two dimensions. The main advantage of this kernel relies in its flexibility because for n=3 it is similar to the standard widely used cubic-spline, whereas for n>3 the interpolating function becomes more centrally condensed, being well suited to track discontinuities such as shock fronts and thermal waves.