混凝土中氯离子扩散的二维分数阶数值分析
Numerical Analysis on the Two-Dimensional Fractional Diffusion Model of Chloride Ion in Concrete
DOI: 10.12677/MOS.2023.125418, PDF,    科研立项经费支持
作者: 蒋 韬, 侍爱玲, 白 羽：北京建筑大学理学院，北京
关键词: 氯离子；扩散；二维；分数阶导数；数值分析；Chloride Ion； Diffusion； Two-Dimensional； Fractional Derivative； Numerical Analysis
摘要: 氯离子对混凝土结构的侵蚀是影响其耐久性的重要原因，而扩散作用是氯离子侵入到混凝土中的最主要方式之一。对于混凝土中氯离子扩散的二维问题，首先基于Caputo分数阶导数建立了变扩散系数的时间分数阶扩散模型，随后结合L1算法建立了数值求解该模型的有限差分格式。接着，利用已有实验数据对分数阶导数的选取进行了分析，并对氯离子在混凝土中的扩散进行了预测。
Abstract: The erosion of chloride ions on concrete structures is an important reason to affect its durability, and diffusion is one of the most important ways for chloride ions to invade concrete. This paper is focusing on the two-dimensional problem of chloride ion diffusion in concrete. Firstly, the temporal fractional diffusion model of Chloride ion with variable diffusion coefficient in concrete is estab-lished based on the Caputo fractional derivative. Next, the finite difference scheme combined with L1 algorithm is established. At last, the value of fractional derivatives is analyzed using existing ex-perimental data, and the diffusion of chloride ions in concrete is predicted.
文章引用：蒋韬, 侍爱玲, 白羽. 混凝土中氯离子扩散的二维分数阶数值分析[J]. 建模与仿真, 2023, 12(5): 4588-4594. https://doi.org/10.12677/MOS.2023.125418

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