Normally, peridynamic (PD) models for transient heat transfer converge, in the limit of the horizon size going to zero, to the solution of the corresponding PDE-based heat transfer. However, different ways of imposing local boundary conditions have been observed to lead to some interesting properties that may deliver the classical solution at a point in space and time from a series of PD solutions obtained with relatively large horizons. Here, we use analytical derivation of PD solutions to explain how approximations introduced by the one-point Gaussian discretization in space (the so-called “meshfree” PD method) and by specific implementations of boundary conditions lead to the intersection of m-convergence curves at the exact value of the corresponding classical model solution. This leads to a strategy of approximating the local solution better with a sequence of PD models that use relatively large horizons compared to a PD model that uses a small horizon. We analyze this property for transient heat conduction in homogeneous and heterogeneous bars. We find that material interfaces influence the intersection of m-convergence curves for transient heat conduction in a 1D heterogeneous bar.

通常，用于瞬态传热的周动力（PD）模型会在视野大小变为零的范围内收敛到相应的基于PDE的传热解决方案。然而，已经观察到施加局部边界条件的不同方式导致了一些有趣的特性，这些特性可能会从在相对较大的视野范围内获得的一系列PD解决方案在时空上的某个点上提供经典解决方案。在这里，我们使用PD解的解析推导来解释空间中的单点高斯离散化（所谓的“无网格” PD方法）和边界条件的特定实现所引入的近似如何导致m的交点。-收敛曲线对应相应经典模型解的精确值。与使用较小视野的PD模型相比，这导致了使用一系列视野相对较大的PD模型更好地逼近局部解的策略。我们分析了均质和非均质钢筋瞬态热传导的这一特性。我们发现材料界面影响一维异质棒中瞬态热传导的m收敛曲线的交点。