Closed SPARSE -- a predictive particle cloud tracer

TL;DR

This paper introduces a closed, predictive particle cloud tracer method called Closed SPARSE, which improves the accuracy of particle cloud tracking by combining Taylor series expansions and statistical averaging, demonstrated through various test cases.

Contribution

The paper presents a closed-form, predictive particle cloud tracer based on the SPARSE formulation, enhancing accuracy and reducing degrees of freedom in particle cloud simulations.

Findings

Demonstrates accuracy and convergence in multiple dimensions

Reduces degrees of freedom in particle cloud tracking

Provides a predictive model for particle cloud trajectories

Abstract

A closed and predictive particle cloud tracer method is presented. The tracer builds upon the Subgrid Particle Averaged Reynolds Stress Equivalent (SPARSE) formulation first introduced in [Davis et al., Proceedings of the Royal Society A, 473(2199), 2017] for the tracing of particle clouds. It was later extended to a Cloud-In-Cell (CIC) formulation in [Taverniers et al., Journal of Computational Physics, 390, 2019] using a Gaussian distribution of a cloud's influence over a mesh-based, velocity field solution. SPARSE corrects the cloud's trace to second order by combining a Taylor series expansion of the drag coefficient and Nusselt number correction factors around the mean relative velocity of a cloud of particles with a Reynolds decomposition of the particle equations to obtain a governing system for the first two statistical moments of the cloud's position, velocity and temperature. Here, we close the thus far unclosed SPARSE formulation by determining the velocity field in the vicinity of the mean cloud location using a truncated Taylor series velocity representation and by combining that with averaging. The resulting tracer is predictive. It enables the tracing of a cloud of particles through a single point and so reduces the required degrees of freedom in the accurate tracing of groups of particles. We demonstrate the accuracy and convergence of the method in several one-, two- and three-dimensional test cases.