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

YAN Qi; LU Zhenhao; WANG Hongjing; FAN Wenping; MA Mingwei; NIU Yanan; WANG Liangjunhao

doi:10.21656/1000-0887.450010

Volume 46 Issue 1

Jan. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(1): 84-91

YAN Qi, LU Zhenhao, WANG Hongjing, FAN Wenping, MA Mingwei, NIU Yanan, WANG Liangjunhao. Applications of a Fractional Diffusion Model With Variable Coefficients in Porous Medium[J]. Applied Mathematics and Mechanics, 2025, 46(1): 84-91. doi: 10.21656/1000-0887.450010

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

doi: 10.21656/1000-0887.450010

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

Funds:

The National Science Foundation of China(11801221)

Received Date: 2024-01-12
Rev Recd Date: 2024-07-24

Abstract

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

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References(16)

References

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