Application of the Chebyshev spectral method to the simulation of groundwater flow and rainfall-induced landslides

摘要

In this paper, the potential of the Chebyshev spectral method (CSM) is examined for the numerical solution of time-dependent variably saturated Darcian flow problems described by the Richards equation (RE). Generally, the computational efficiency of the traditional finite difference method (FDM) is not high because it requires a high mesh density to improve accuracy. Therefore, the Chebyshev spectral method (CSM) was extended to model groundwater transient flow in unsaturated soils. Furthermore, the Gardner model (soil-water characteristic curve) was adopted to linearize the RE for an inclined slope. The test results demonstrated that the accuracy, efficiency, and robustness of the CSM are better than those of the traditional FDM. A comparison of the analytical solutions of each method showed that the computational accuracy (L_2(h*)) of the CSM was less affected by the grid size than that of the FDM. Simultaneously, the CSM was not sensitive to the initial conditions. The results demonstrated that the numerical accuracy of the CSM was stable in the order of 10~(-6) to 10~(-7), whereas that of the FDM was in the order of 10~(-3) to 10~(-6); it achieved higher accuracy with fewer grid points. The CSM was successfully applied to solve the one-dimensional transient flow problem on unsaturated soil slopes. The numerical results indicated that the proposed method solved the transient flow problem related to rainfall-induced landslides with high accuracy. This proposed approach can be developed to analyze rainfall-induced landslides.