A novel 2D diffusion model for composite domain with non-regularly shaped interface

This paper presents a new two-dimensional transient diffusion model adapted to composite domains with non-regular internal interfaces. The model employs a finite difference approach based on the explicit DuFort–Frankel scheme, coupled with the Ghost Fluid Method, to ensure both numerical efficiency and accurate interface treatment. Discontinuities in field values and fluxes across subdomains are captured using mesh-aligned directional approximations, allowing the computation to remain on a regular Cartesian grid.The numerical scheme is first validated against an analytical solution, demonstrating second-order accuracy in both space and time. Additional validation is performed through comparison with a finite element model under realistic thermal boundary conditions relevant to building physics.The model is subsequently applied to the optimization of the interface geometry between two materials in a building wall, exposed to spatially heterogeneous conditions typical of an urban canyon environment. Thermal performance is assessed using two distinct cost functions. Although the average improvements over annual and monthly timescales are moderate, the model identifies significant instantaneous performance gains at the hourly scale.