Numerical framework for optimizing the thermal performance of building walls with shaped interfaces between material layers

This work investigates the impact of interface geometry between concrete and insulating layers on the energy performance of building walls. A numerical efficient two-dimensional transient heat transfer model based on finite differences with the dufort-frankel scheme and the Ghost Fluid Method is developed to simulate annual wall thermal response. Interface shapes are parametrically defined using explicit mathematical functions and particle-based approaches, including bézier and Radial Basis Function curves, and optimized using the NSGA-II genetic algorithm. The approach is applied to a double-layer building façade with external insulation under spatially and temporally heterogeneous boundary conditions in urban street canyon environments. Several studies assess the influence of interface parametrization, identify the most suitable representation, and extend the analysis to multiple street canyon configurations across metropolitan France. Results demonstrate that optimized interface geometries can significantly improve annual energy efficiency and that optimal shapes are highly sensitive to environmental conditions.