Gurzadyan's Problem 5 and improvement of softenings for cosmological simulations using the PP method

TL;DR

This paper explores modifications to standard gravitational softenings in cosmological simulations, demonstrating improved accuracy and potential for higher precision in particle-particle methods.

Contribution

It introduces new softenings that enhance accuracy in cosmological simulations, addressing Gurzadyan's Problem 5 and improving computational standards.

Findings

Modified softenings achieve near-Newtonian accuracy

Force resolution can be increased to half the minimum interparticle distance

Enhanced softenings enable higher-precision cosmological simulations

Abstract

This paper is devoted to different modifications of two standard softenings of the gravitational attraction (namely the Plummer and Hernquist softenings), which are commonly used in cosmological simulations based on the particle-particle (PP) method, and their comparison. It is demonstrated that some of the proposed alternatives lead to almost the same accuracy as in the case of the pure Newtonian interaction, even despite the fact that the force resolution is allowed to equal half the minimum interparticle distance. The revealed way of precision improvement gives an opportunity to succeed in solving Gurzadyan's Problem 5 and bring modern computer codes up to a higher standard.