Numerical approach for modeling fractal mobile/immobile transport model in porous and fractured media

By Omid Nikan, J. Machado, Ahmad Golbabai, T. Nikazad. 2020

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Abstract The fractal mobile/immobile model of the solute transport is based on the assumption that the waiting times in the immobile region follow a power-law, and this leads to the application of fractional time derivatives. The model covers a wide family of systems that include heat diffusion and ocean acoustic propagation. This paper develops an efficient computational technique, stemming from the radial basis function-generated finite difference (RBF-FD), to solve the fractal mobile-immobile transport model (FMTM). The time fractional derivative of the FMTM is discretized via the shifted Grunwald-Letnikov formula with second-order accuracy. On the other hand, the spatial derivative is approximated using the local RBF-FD method. The main benefit of the local collocation technique is that we only need to consider discretization points present in each of the sub-domains around the collocation point. The stability and convergence analysis of the proposed method are proven via the energy method in the L2 space. The numerical results for the FMTM on regular and irregular domains confirm the theoretical formulation and efficiency of the proposed scheme.

Subfields: Computational Mechanics, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/70e52e7a13f174ccf4d2c21e65b57c1d1ba15cb4