Response Effects Due to Polygonal Representation of Fillers In Composite Media Thermal Models

Physics models of engineering systems often require geometric representations of complex physical domains. When smooth or detailed features are simplified for model construction or meshing, the resulting geometric defeaturing can introduce a form of model error that is distinct from numerical discretization error. This work investigates that effect for a two-dimensional composite unit cell containing a centered circular filler that is represented by regular polygons with 3 to 26 sides. The system response quantity is the dimensionless effective thermal conductivity, k*, evaluated over fill fractions from 1% to 78% and filler-to-matrix thermal-conductivity ratios from 0 to 100. Code verification is performed using the Method of Manufactured Solutions, and solution verification is performed using a global-deviation grid convergence index to estimate numerical uncertainty in k*. The geometric-fidelity effect is then quantified by comparing each polygonal representation with a 26-sided reference representation and by interpreting this difference relative to the estimated numerical uncertainty. The results show that geometric representation can materially affect k* Across the full ensemble, 1981 of 2016 fine-mesh cases had relative numerical uncertainty Unum/k* below 1%, with a median value of 0.02%, while low-sided polygon cases often exceeded the 1% geometric-convergence threshold.