Effective transport properties of conformal Voronoi-bounded columns via recurrent boundary element expansions

TL;DR

This paper introduces a boundary element method with recurrent series to accurately compute high-order transport parameters in complex 2D microstructures like Voronoi tessellations, improving understanding of their effective properties.

Contribution

It presents a novel recurrent boundary element approach for efficient high-order parameter calculation in polygonal and conformal prism structures within Voronoi tessellations.

Findings

Proximity to simpler estimates linked to centroidal VT and compactness.

The method accurately captures high-order parameters.

Identified an error in previous triangular lattice data.

Abstract

Effective transport properties of heterogeneous structures are predicted by geometric microstructural parameters, but these can be difficult to calculate. Here, a boundary element code with a recurrent series method accurately and efficiently determines the high order parameters of polygonal and conformal prisms in regular two-dimensional lattices and Voronoi tessellations (VT). This reveals that proximity to simpler estimates is associated with: centroidal VT (cf random VT), compactness, and VT structures (cf similarly compact semi-regular lattices). An error in previously reported values for triangular lattices is noted.