Finite difference method for space-fractional seepage process in unsaturated soil

The transport process and seepage properties of underground water in unsaturated soil are of great research significance. Firstly, the transport process of underground water in unsaturated soil in an anomalous diffusion perspective is analyzed, and by involving the Conformable derivative, the space-fractional anomalous diffusion equation in one-dimensional situation is derived. Secondly, the discretization schemes of this seepage equation are derived by using the full-implicit finite difference method. The iterative matrix of numerical modelling is derived as well. In the end, the effectiveness of the numerical solution in the space-fractional anomalous diffusion equation is verified by comparing the numerical solution with the experimental data in the existing paper. In addition, the sensitivity of the parameters in the seepage equation is analyzed. The results show that the new model can well characterize the transport process of underground water in unsaturated soil, and the Conformable derivative is suitable for this method.