Heat losses through the building envelope is one of the key factors in the calculation of the building energy balance. If steady-state heat conduction is observed, which is commonly used to assess the heat losses in building, there is an analytical solution for one-dimensional problem. For two and three-dimensional problems, especially for the complex geometry cases, one must use numerical methods to solve the heat conduction equation. To standardise two and three-dimensional calculation of heat losses through building elements, ISO 10211 standard can be used. The standard has four benchmark examples with criteria that must be satisfied to declare a method as a high-precision calculation method. A problem occurs for Case 1 of benchmark test because the analysed problem has a singular point due to discretely assigned Dirichlet boundary conditions. The reliability of the results around the singular point could be improved by the refinement of the mesh in the area around the singular point, but as a point of interest is the total heat flux that is entering the building element, and it must converge between subdivisions, this method is not good since the reliable result cannot be reached. The problem for the convergence is in the marginal node because the temperature gradient in it increases as the temperature difference remains constant and the distance between the corresponding nodes decreases. For that reason, Case 1 from the benchmark is inadequate because even if there is a discontinuity in temperature field on the boundary, there is an interval in which this change is to happen, and the heat flux has a theoretical limit which is not infinity. From the results of this research, it is shown that one should neglect a certain number of singular points in order to achieve the tolerance given by the standard since the temperature further from the marginal node is stable for any subdivision.

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计算建筑构件 2d 和 3d 热损失时的总热通量收敛

通过建筑围护结构的热损失是计算建筑能量平衡的关键因素之一。如果观察到常用于评估建筑物热损失的稳态热传导，那么一维问题就有解析解。对于二维和三维问题，特别是复杂几何的情况，必须用数值​​方法求解热传导方程。为了标准化建筑构件热损失的二维和三维计算，可以使用 ISO 10211 标准。该标准有四个基准示例，其标准必须满足才能将方法声明为高精度计算方法。基准测试的案例 1 出现问题，因为分析的问题由于离散分配 Dirichlet 边界条件而具有奇异点。奇异点周围结果的可靠性可以通过在奇异点周围区域中细化网格来提高，但作为一个关注点是进入建筑元素的总热通量，它必须在细分之间收敛，这种方法不好，因为无法达到可靠的结果。收敛的问题在于边缘节点，因为随着温差保持恒定和相应节点之间的距离减小，边缘节点中的温度梯度增加。出于这个原因，来自基准的案例 1 是不充分的，因为即使边界上的温度场存在不连续性，也存在发生这种变化的区间，并且热通量的理论极限不是无穷大。从这项研究的结果来看，