Fractional Convection
Fractional Convection
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部分对流
DOI：
10.1115/1.4037414
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发表时间：
2018-01-01
影响因子：
2
通讯作者：
Kurths, Juergen
中科院分区：
文献类型：
--
作者：
Li, Changpin;Yi, Qian;Kurths, Juergen
本文首次描述了分数阶对流算子，并给出了其二阶收敛的离散形式。建立了分数对流扩散方程的数值格式，以便直观地了解分数对流的行为。然后，我们研究了从未被考虑过的分数对流占主导的扩散方程，它的扩散是正态的，并且用拉普拉斯函数来表征。通过数值模拟，观察到有趣的分数对流现象。此外，我们还首次研究了分数阶对流主导扩散方程，其中对流和扩散都是分数阶意义上的。相应的分数对流现象也通过计算机图形显示出来。
In this study, we describe the fractional convection operator for the first time and present its discrete form with second-order convergence. A numerical scheme for the fractional-convection-diffusion equation is also constructed in order to get insight into the fractional convection behavior visually. Then, we study the fractional-convection-dominated diffusion equation which has never been considered, where the diffusion is normal and is characterized by the Laplacian. The interesting fractional convection phenomena are observed through numerical simulation. Moreover, we investigate the fractional-convection-dominated-diffusion equation which is studied for the first time either, where the convection and the diffusion are both in the fractional sense. The corresponding fractional convection phenomena are displayed via computer graphics as well.