Application of RBF-DQ Method to Time-Dependent Analysis of Unsaturated Seepage
Date of Original Version
Richards’ equation is a nonlinear partial differential equation governing unsteady seepage flow through unsaturated porous media. This paper investigates applicability of radial basis function-based differential quadrature (RBF-DQ), as a meshless method, to simulate one-dimensional flow processes in the unsaturated zone under different initial and boundary conditions. Fourth-order Runge–Kutta scheme has been adopted for time integration. Results of solving three numerical examples using RBF-DQ are compared with those of analytical, numerical, and experimental solutions presented in the literature. The comparison indicates that RBF-DQ can provide more accurate results comparing with traditional FDM or FEM without the need to discretize the computational domain. Moreover, the merit of mesh-free characteristic in RBF-DQ makes it suitable not only for solving nonlinear problems but also for dealing with multidimensional problems since meshless methods are not restricted to dimensional limitations. A key parameter in utilizing multiquadratic approximation in RBF-DQ method is the user-defined shape parameter C, which may significantly affect solution accuracy. Thus, a sensitivity analysis has been conducted to study possible effects of shape parameter on achieved results.
Transport in Porous Media
Motaman, F., G. R. Rakhshandehroo, M. R. Hashemi, and M. Niazkar. "Application of RBF-DQ Method to Time-Dependent Analysis of Unsaturated Seepage." Transport in Porous Media 125, 3 (2018): 543-564. doi:10.1007/s11242-018-1138-7.