变系数分数阶扩散模型在多孔介质中的应用

颜琪; 鲁祯昊; 王虹静; 范文萍; 马铭伟; 牛雅楠; 王梁俊豪

doi:10.21656/1000-0887.450010

变系数分数阶扩散模型在多孔介质中的应用

doi: 10.21656/1000-0887.450010

江南大学理学院, 江苏无锡 214122

基金项目:

国家自然科学基金 11801221

江苏省自然科学基金 BK20180586

详细信息

作者简介:
颜琪(2003—)，男，本科生(E-mail: 1131210324@stu.jiangnan.edu.cn)

通讯作者:
范文萍(1990—)，女，副教授，博士(通讯作者. E-mail: wpfan@jiangnan.edu.cn)

中图分类号: O29
计量
- 文章访问数: 34
- HTML全文浏览量: 17
- PDF下载量: 4
- 被引次数: 0
出版历程
- 收稿日期: 2024-01-12
- 修回日期: 2024-07-24
- 刊出日期: 2025-01-01

Applications of a Fractional Diffusion Model With Variable Coefficients in Porous Medium

School of Science, Jiangnan University, Wuxi, Jiangsu 214122, P.R.China

摘要

摘要: 针对多孔介质中的反常扩散行为, 提出了利用变系数的时间分数阶扩散模型模拟煤炭介质中甲烷的反常扩散现象. 将常系数时间分数阶分形扩散模型推广至变系数情形, 并建立了变系数分数阶模型的非均匀网格数值求解格式；在模型数值解的基础上, 基于实验测量数据, 提出了高效的布谷鸟搜索算法, 同时估计了模型中的多个重要参数. 最后通过数值实验, 验证了变系数分数阶扩散模型及布谷鸟算法在研究多孔介质中反常扩散现象正反问题中的有效性.
- 变系数分数阶扩散模型 /
- 数值格式 /
- 多参数识别 /
- 布谷鸟算法
Abstract: Aimed at the anomalous diffusion behavior in porous medium, a time fractional diffusion model with variable coefficients was proposed to simulate the anomalous diffusion of methane in coal medium. The time fractional fractal diffusion model with constant coefficients was extended to the case with variable coefficients, the numerical scheme based on graded meshing of the fractional model with variable coefficients was established. Based on the numerical solution and experimental data, an efficient cuckoo search algorithm was proposed to estimate several important parameters in the model. Finally, the effectiveness of the fractional diffusion model with variable coefficients and the cuckoo search algorithm in studying the direct and inverse problems of anomalous diffusion in porous media, was verified with numerical experiments.
- fractional diffusion model with variable coefficients /
- numerical scheme /
- multi-parameter identification /
- cuckoo search algorithm

HTML全文

图 1 变系数时间分数阶扩散模型的(α, d_f, θ, β)参数迭代结果

Figure 1. Parameter (α, d_f, θ, β) iteration results of the time fractional diffusion model with variable coefficients

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图 2 变系数时间分数阶扩散模型的数据拟合图

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 2. Data fittings of the time fractional diffusion model with variable coefficients

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图 3 变系数时间分数阶扩散模型的(α, d_f, θ, β)参数迭代结果

Figure 3. Parameter (α, d_f, θ, β) iteration results of the time fractional diffusion model with variable coefficients

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图 4 布谷鸟搜索算法的适应度函数图

Figure 4. The fitness function of the cuckoo search algorithm

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图 5 快速格式的计算时间

Figure 5. The calculation time of the fast scheme

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