Spatial homogenization algorithm for bridging disparities in scale between the fire and solid domains

The analysis of structures exposed to non-uniform heating from localized fires is a challenging task due to the spatially varying boundary conditions and the differences in scale between the fire simulation and solid heat transfer model. This paper presents a spatial homogenization algorithm for capturing non-uniform boundary conditions from a high-resolution fire simulation in a low-resolution finite element heat transfer model of a structure. The homogenization algorithm uses numerical integration by the trapezoid rule to calculate the equivalent thermal flux vector in the finite element heat transfer model for a spatially varying surface flux. The proposed method is compared to other approximating techniques, including averaging, sampling, and least squares methods, for a 2D heat transfer problem. The results demonstrate that the proposed homogenization algorithm converges rapidly due to the energy-equivalent representation of the thermal boundary condition. The homogenization algorithm is then implemented in a 3D heat transfer model that uses macro-level plate elements. For an application involving a horizontal plate exposed to a localized fire, the model is shown to converge to the results obtained by a solid finite element model. The homogenization algorithm combined with the plate heat transfer element proves to be an accurate and highly efficient means for analyzing structures with spatially varying thermal boundary conditions calculated by computational fluid dynamics.