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Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model

机译：具有广义Cattaneo模型的多孔介质分数热传导的数值方法

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摘要

The generalized Cattaneo model describes the heat conduction system in the perspective of time-nonlocality. This paper proposes an accurate and robust meshless technique for approximating the solution of the time fractional Cattaneo model applied to the heat flow in a porous medium. The fractional derivative is formulated in the Caputo sense with order 1 ＜α＜2. First, a finite difference technique of convergence order Ο(δt~(3-α)) is adopted to achieve the temporal discretization. The unconditional stability of the method and its convergence are analysed using the discrete energy technique. Then, a local meshless method based on the radial basis function partition of unity collocation is employed to obtain a full discrete algorithm. The matrices produced using this localized scheme are sparse and, therefore, they are not subject to ill-conditioning and do not pose a large computational burden. Two examples illustrate in computational terms of the accuracy and effectiveness of the proposed method.
机译：广义的Cattaneo模型在时间 - 非划分的角度描述了导热系统。本文提出了一种精确且鲁棒的无纤维技术，用于近似施加到多孔介质中热流的时间分数Cattaneo模型的解决方案。分数衍生物与顺序1 <α<2的Caputo感应配制。首先，采用收敛顺序ο（ΔT〜（3-α））的有限差分技术来实现时间离散化。使用离散能量技术分析该方法及其收敛的无条件稳定性。然后，采用基于径向基函数分区的Unity搭配的本地无网格方法来获得完整的离散算法。使用该局部方案产生的基质稀疏，因此，它们不受残疾的影响，并且不会造成大的计算负担。两个示例在所提出的方法的准确性和有效性的计算方面说明。

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