Abstract A new Lagrangian non-local diffusion model, designed as a meshless particle simulation method, is proposed to predict the thermal response of solids involving discontinuous. The main idea is to understand the heat transfer process of solids via a Lagrangian treatment of a particle-discretized system, which provides a more general physical representation of the heat transfer process of solids. In contrast to the traditional differential model, the proposed mathematical model is expressed via an integral form, which can easily handle the case involving discontinuities. The spatial convergence studies show that the proposed model converges to its associated non-local solution while increasing the number of particles in a fixed cut-off radius; and it can reach the local exact solution when the cut-off radius is close to zero. The numerical examples not only verify that the proposed diffusion model converges to the continuum heat conduction model, but also show the capability of its application to heat transfer problems involving discontinuities. In particular, the computational performance of the proposed non-local thermal model is also demonstrated its computational performance in the case with practical crack propagation in a two-dimensional plate. In addition, the specific comparison between the proposed method and the well-developed peridynamics approach for heat conduction problems is carefully described with rigor via mathematical proofs and numerical results. Specifically, the proposed model is shown to be a variation of the corresponding peridynamic-type thermal diffusion model. This model not only has a formulation consistent with that of peridynamics in solid mechanics but also shows a better performance in the case with sharp corners than that of the peridynamic diffusion in [1].

中文翻译：

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基于拉格朗日粒子法的不连续固体中的非局部热传递模型

摘要 提出了一种新的拉格朗日非局部扩散模型，设计为一种无网格粒子模拟方法，用于预测不连续固体的热响应。主要思想是通过粒子离散系统的拉格朗日处理来理解固体的传热过程，这提供了固体传热过程的更一般的物理表示。与传统的微分模型相比，所提出的数学模型采用积分形式表示，可以轻松处理涉及不连续性的情况。空间收敛研究表明，所提出的模型收敛到其相关的非局部解，同时增加了固定截止半径内的粒子数量；当截断半径接近于零时，可以达到局部精确解。数值例子不仅验证了所提出的扩散模型收敛于连续热传导模型，而且展示了其应用于涉及不连续性的传热问题的能力。特别是，所提出的非局部热模型的计算性能也证明了其在二维板中实际裂纹扩展的情况下的计算性能。此外，通过数学证明和数值结果，对所提出的方法与针对热传导问题的成熟近场动力学方法之间的具体比较进行了详细的描述。具体而言，所提出的模型被证明是相应的近场动力学型热扩散模型的变体。