Accurate predictions of chaotic motion of a free fall disk

TL;DR

This paper introduces the Clean Numerical Simulation (CNS) strategy to accurately predict the chaotic motion of a free fall disk in fluid, overcoming limitations of traditional numerical algorithms in long-term trajectory prediction.

Contribution

The paper presents CNS as a novel method capable of reliably predicting long-term chaotic trajectories, surpassing traditional double precision algorithms.

Findings

CNS yields convergent, reliable trajectories over long durations.

Traditional algorithms produce disparate results in chaotic systems.

CNS accurately predicts behavior near bifurcation points.

Abstract

It is important to know the accurate trajectory of a free fall object in fluid (such as a spacecraft), whose motion might be chaotic in many cases. However, it is impossible to accurately predict its chaotic trajectory in a long enough duration by traditional numerical algorithms in double precision. In this paper, we give the accurate predictions of the same problem by a new strategy, namely the Clean Numerical Simulation (CNS). Without loss of generality, a free fall disk in water is considered, whose motion is governed by the Andersen-Pesavento-Wang model. We illustrate that convergent and reliable trajectories of a chaotic free fall disk in a long enough interval of time can be obtained by means of the CNS, but different traditional algorithms in double precision give disparate trajectories. Besides, unlike the traditional algorithms in double precision, the CNS can predict the accurate posture of the free fall disk near the vicinity of the bifurcation point of some physical parameters in a long duration. Therefore, the CNS can provide reliable prediction of chaotic systems in a long enough interval of time.