期刊
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER
卷 111, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.icheatmasstransfer.2019.104443
关键词
Riemann-Liouville fractional derivative; Fractal mobile/immobile transport model; RBF-FD; Stability; Convergence
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 L-2 space. The numerical results for the FMTM on regular and irregular domains confirm the theoretical formulation and efficiency of the proposed scheme.
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