An efficient, second order method for the approximation of the Basset history force

TL;DR

This paper introduces a novel second-order numerical method that significantly improves the efficiency and accuracy of computing the Basset history force in particle-fluid interaction simulations, enabling more reliable turbulence statistics.

Contribution

A new exponential approximation-based numerical method for the Basset force that reduces computational cost and enhances accuracy and stability in particle simulations.

Findings

Reduces CPU time and memory by over an order of magnitude.

Increases accuracy of Basset force computation by an order of magnitude.

Provides more reliable statistical data in turbulence simulations.

Abstract

The hydrodynamic forces exerted by a fluid on small isolated rigid spherical particles are usually well described by the Maxey-Riley (MR) equation. The most time-consuming contribution in the MR equation is the Basset history force which is a well-known problem for many-particle simulations in turbulence. In this paper a novel numerical approach is proposed for the computation of the Basset history force based on the use of exponential functions to approximate the tail of the Basset force kernel. Typically, this approach not only decreases the cpu time and memory requirements for the Basset force computation by more than an order of magnitude, but also increases the accuracy by an order of magnitude. The method has a temporal accuracy of O(Delta t^2) which is a substantial improvement compared to methods available in the literature. Furthermore, the method is partially implicit in order to increase stability of the computation. Traditional methods for the calculation of the Basset history force can influence statistical properties of the particles in isotropic turbulence, which is due to the error made by approximating the Basset force and the limited number of particles that can be tracked with classical methods. The new method turns out to provide more reliable statistical data.