An optimised logarithmic discretisation approach for accurate and efficient compact thermal models

The accuracy of building energy simulations is of considerable interest as discrepant results can elicit adverse financial and environment consequences. The physical and temporal scales considered within building energy applications necessitate compact modelling approaches. The prediction accuracy of such simulations is intrinsically linked with the ability to predict the thermal responses of structural elements. The optimal means of representing these components such that accurate solutions are ensured at minimal computational cost remains unclear. The current study seeks to optimise the spatial placement of nodes through assessing and reporting results pertaining to a logarithmic spatial discretisation method. Contour plots are presented to intuitively determine optimal discretisation levels and time steps required for accurate thermal response predictions. This is achieved by comparing numerical solutions of varying discretisation levels with benchmark analytical solutions. Results are reported in terms of governing dimensionless parameters, Biot and Fourier numbers, to ensure generality of findings. Furthermore, spatial and temporal discretisation errors are separated and assessed independently. Finally, models derived using the proposed guidance achieve high levels of prediction accuracy for typically encountered boundary conditions with buildings.