Abstract Numerical simulation of heat conduction in the concrete structure with cooling pipes is meaningful and full of challenges. In this paper, the radial basis function finite difference method (RBF-FD) combined with a self-correcting prediction model (SCM) is proposed for thermal analysis of heat transfer in concrete structures with pipe cooling system. Using the Multiquadric radial basis function (MQ-RBF), the SCM is proposed to give full play to advantages of the localized meshless method. This technique allows use of more number of nodes in the whole domain to solve the ill-conditioning problem associated with multiple regions of rapid variation and increases the accuracy of models. A multiple-scale technique is applied to determine the shape parameter in the MQ-RBF and the fictitious nodes method is modified by using just one fictitious node outside the domain to deal with boundary conditions of the third kind in tiny holes. To show the flexibility and efficiency of the proposed scheme, we consider several examples with different number, size, and positions of pipes. Meanwhile, a guidance of determination of effected area near a tiny hole is provided and a simple optimization design of cooling pipe system is performed. The results demonstrate advantages of the proposed model which can effectively handle heat conduction problem with multiple holes subjected to the third kind boundary conditions.

中文翻译：

---

无网格RBF-FD方法结合间接模型管冷混凝土结构传热热分析

摘要 带冷却管的混凝土结构热传导的数值模拟具有重要意义且充满挑战。在本文中，径向基函数有限差分法 (RBF-FD) 结合自校正预测模型 (SCM) 被提出用于管道冷却系统混凝土结构传热的热分析。利用多二次径向基函数（MQ-RBF），提出了SCM，以充分发挥局部无网格方法的优点。这种技术允许在整个域中使用更多数量的节点来解决与多个快速变化区域相关的病态问题，并提高模型的准确性。采用多尺度技术确定MQ-RBF中的形状参数，并修改了虚拟节点方法，仅使用域外的一个虚拟节点来处理小孔中的第三类边界条件。为了显示所提出方案的灵活性和效率，我们考虑了几个具有不同数量、尺寸和位置的管道的例子。同时，对微孔附近影响区域的确定提供了指导，并对冷却管道系统进行了简单的优化设计。结果证明了所提出模型的优点，该模型可以有效地处理受第三类边界条件影响的多孔热传导问题。为了显示所提出方案的灵活性和效率，我们考虑了几个具有不同数量、尺寸和位置的管道的例子。同时，对微孔附近影响区域的确定提供了指导，并对冷却管道系统进行了简单的优化设计。结果证明了所提出模型的优点，该模型可以有效地处理受第三类边界条件影响的多孔热传导问题。为了显示所提出方案的灵活性和效率，我们考虑了几个具有不同数量、尺寸和位置的管道的例子。同时，对微孔附近影响区域的确定提供了指导，并对冷却管道系统进行了简单的优化设计。结果证明了所提出模型的优点，该模型可以有效地处理受第三类边界条件影响的多孔热传导问题。