Abstract A two-dimensional model is proposed for energy efficiency assessment through the simulation of heat transfer in building envelopes, considering the influence of the surrounding environment. The model is based on the Du Fort–Frankel approach that provides an explicit scheme with a relaxed stability condition. The model is first validated using an analytical solution and then compared to three other standard schemes. Results show that the proposed model offers a good compromise in terms of high accuracy and reduced computational efforts. Then, a more complex case study is investigated, considering non-uniform shading effects due to the neighboring buildings. In addition, the surface heat transfer coefficient varies with wind velocity and height, which imposes an addition non-uniform boundary condition. After showing the reliability of the model prediction, a comparison over almost 120 cities in France is carried out between the two- and the one-dimensional approaches of the current building simulation programs. Important discrepancies are observed for regions with high magnitudes of solar radiation and wind velocity. Last, a sensitivity analysis is carried out using a derivative-based approach. It enables to assess the variability of the solution according to the modeling of the two-dimensional boundary conditions. Moreover, the proposed model computes efficiently the solution and its sensitivity to the modeling of the urban environment.

中文翻译：

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一种有效的建筑围护结构二维传热模型

摘要 考虑周围环境的影响，通过对建筑围护结构传热的模拟，提出了一种能效评估的二维模型。该模型基于 Du Fort-Frankel 方法，该方法提供了具有宽松稳定性条件的显式方案。该模型首先使用解析解进行验证，然后与其他三个标准方案进行比较。结果表明，所提出的模型在高精度和减少计算工作量方面提供了良好的折衷。然后，研究了一个更复杂的案例研究，考虑到由于相邻建筑物造成的非均匀阴影效应。此外，表面传热系数随着风速和高度的变化而变化，这增加了非均匀边界条件。在显示模型预测的可靠性后，对法国近120个城市的当前建筑模拟程序的二维和一维方法进行了比较。对于具有高强度太阳辐射和风速的地区，观察到了重要的差异。最后，使用基于导数的方法进行敏感性分析。它能够根据二维边界条件的建模来评估解的可变性。此外，所提出的模型有效地计算了解决方案及其对城市环境建模的敏感性。对于具有高强度太阳辐射和风速的地区，观察到了重要的差异。最后，使用基于导数的方法进行敏感性分析。它能够根据二维边界条件的建模来评估解的可变性。此外，所提出的模型有效地计算了解决方案及其对城市环境建模的敏感性。对于具有高强度太阳辐射和风速的地区，观察到了重要的差异。最后，使用基于导数的方法进行敏感性分析。它能够根据二维边界条件的建模来评估解的可变性。此外，所提出的模型有效地计算了解决方案及其对城市环境建模的敏感性。