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首页> 外文期刊>International Journal of Heat and Mass Transfer >Modeling heat transfer subject to inhomogeneous Neumann boundary conditions by smoothed particle hydrodynamics and peridynamics
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Modeling heat transfer subject to inhomogeneous Neumann boundary conditions by smoothed particle hydrodynamics and peridynamics

机译：通过平滑粒子流体动力学和周动力学，对不均匀诺伊曼边界条件下的传热进行建模

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摘要

Nonzero fluxes going through boundaries interfaces are normally observed in heat transfer, which in general can be described as inhomogeneous Neumann boundary conditions (BCs). Both smoothed particle hydrodynamics (SPH) and peridynamics have been employed for modeling heat transfer or thermal diffusion processes. The former is a numerical method used to approximate the solutions of classical heat diffusion PDEs. The latter provides a nonlocal model for heat diffusion. They both employ a nonlocal formulation, which requires a full support of the nonlocal kernel to ensure accuracy. In this work, we propose a new, higher-order method to enforce inhomogeneous Neumann BCs in SPH and peridynamic model for heat transfer problems. In that, fictitious layers of (ghost) particles are needed to guarantee full support of the nonlocal kernel. The temperature is extrapolated to the ghost particles based on the Taylor expansion and the BC to be imposed. By such, no additional term is introduced into the heat equation; meanwhile, the numerical solutions converge to the classical solutions with notably improved accuracy. To validate, assess, and demonstrate the proposed method, we simulate different transient or steady heat transfer problems subject to linear or nonlinear BCs, including heat conduction, natural convection, and presence of insulated cracks. The numerical results are compared with the exact solutions of classical PDEs, solutions of other numerical methods, or experimental data. (C) 2019 Elsevier Ltd. All rights reserved.
机译：通常在传热过程中会观察到穿过边界界面的非零通量，这通常可以描述为非均匀诺伊曼边界条件（BCs）。平滑粒子流体动力学（SPH）和周动力学都已用于模拟传热或热扩散过程。前者是一种用于近似经典热扩散PDE解的数值方法。后者提供了热扩散的非局部模型。它们都采用非本地公式，这需要非本地内核的完全支持以确保准确性。在这项工作中，我们提出了一种新的，更高阶的方法来在SPH和换热问题的动力学模型中强制执行不均匀的Neumann BC。这样，就需要虚拟的（虚幻）粒子层来保证对非本地内核的完全支持。基于泰勒膨胀和要施加的BC，将温度外推到幻影颗粒。这样，在热方程中没有引入任何附加项。同时，数值解收敛到经典解，且精度大大提高。为了验证，评估和证明所提出的方法，我们模拟了受线性或非线性BC影响的各种瞬态或稳态传热问题，包括热传导，自然对流和存在绝缘裂纹。将数值结果与经典PDE的精确解，其他数值方法的解或实验数据进行比较。 （C）2019 Elsevier Ltd.保留所有权利。

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