Deterministic drag modelling for spherical particles in Stokes regime using data-driven approaches

Abstract

In this paper, we develop a deterministic drag model for stationary spherical particles in a Stokes flow using a cascade of data-driven approaches. The model accounts for the variation in drag experienced by each particle within fixed random arrangements. The developed model is a symbolic expression that offers explainability, ease of implementation, and computational efficiency. Firstly, we generate particle-resolved direct numerical simulation data of the flow past periodic random arrangements of stationary spherical particles with volume fractions between 0.05 and 0.4 using the method of regularized Stokeslets. Secondly, we train graph neural networks (GNs) on the generated data to learn the pairwise influence of neighbouring particles on a reference particle. The GNs are converted to symbolic expressions using genetic programming (GP), unveiling repeated subexpressions. Finally, these subexpressions constitute the foundation of the proposed algebraic model, further refined via non-linear regression. The proposed model can qualitatively mimic the pairwise influences as predicted by the GN and can capture the drag variations with accuracy from 74% and up to 84.7% when compared to the particle-resolved simulations. Due to the interpretability of the proposed model, we are able to explore how neighbour positions alter the drag of a particle in an assembly. The proposed model is a promising tool for studying the dynamics of particle assemblies in Stokes flow.