论文标题
通过建筑元素计算2D和3D热量损失的总热通量收敛
Total heat flux convergence in the calculation of 2d and 3d heat losses through building elements
论文作者
论文摘要
通过建筑物包络的热量损失是计算建筑物能量平衡的关键因素之一。如果观察到稳态热传导（通常用于评估建筑物中的热量损失），则有一个分析解决方案用于一维问题。对于两维问题，尤其是对于复杂的几何情况，必须使用数值方法来求解热传导方程。为了通过建筑元素对热量损失进行标准化，可以使用ISO 10211标准。该标准具有四个具有标准的基准示例，必须满足将方法声明为高精度计算方法。基准测试的病例1发生问题，因为分析的问题由于离散分配的Dirichlet边界条件而具有单数点。通过在奇异点周围的区域中的网格的细化，可以提高奇异点周围结果的可靠性，但是作为关注点是进入建筑元素的总热通量，并且必须在细分之间融合，因此该方法不好，因为无法达到可靠的结果。收敛的问题在于边缘节点，因为它的温度梯度随着温度差保持恒定而增加，相应节点之间的距离降低。因此，从基准测试的情况1是不充分的，因为即使边界上的温度场存在不连续性，也存在这种变化的间隔，并且热通量的理论极限不是无限的。从这项研究的结果来看，应该忽略一定数量的单数点，以达到标准给出的公差，因为任何细分都远离边缘节点的温度是稳定的。
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.
