A novel 2D diffusion model for composite domain with non-regularly shaped interface
Abstract
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.
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BibTeX
@article{dumontaud2026novel,
title = {{A novel 2D diffusion model for composite domain with non-regularly shaped interface}},
author = {William Dumontaud and Julien Berger and Benjamin Kadoch},
journal = {Computers \& Mathematics with Applications},
year = {2026},
month = sep,
doi = {10.1016/j.camwa.2026.06.007},
url = {https://hal.science/hal-05679840v2},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - A novel 2D diffusion model for composite domain with non-regularly shaped interface
AU - William Dumontaud
AU - Julien Berger
AU - Benjamin Kadoch
PY - 2026
DA - 2026/09/01
JO - Computers & Mathematics with Applications
DO - 10.1016/j.camwa.2026.06.007
UR - https://hal.science/hal-05679840v2
AB - 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.
SN - 0898-1221
ER -