An improved Picard iteration scheme for simulating unsaturated flow in porous media

Abstract

The Richards equation is widely used in the simulation of unsaturated flow and related fields. In the numerical solution process, the finite volume method can be used to carry out numerical discretization, and the Picard method is used for iterative solution. However, in order to obtain a more reliable numerical solution, the space step size of the conventional uniform grid is often small. Especially under some unfavorable numerical conditions, such as infiltration into dry soil and layered soil with very different hydraulic conductivity, this will be very time-consuming and even slow to converge. Thus, combined with the non-uniform grid in the form of Chebyshev, an improved Picard method based on the non-uniform two-grid correction scheme (NTG-PI) is proposed to model 1D unsaturated flow in porous media. Through three examples of unsaturated flow under unfavorable conditions, the proposed scheme was verified. The results show that, compared with the conventional Picard method, NTG-PI can obtain higher numerical accuracy with a smaller number of nodes, and also has a faster convergence rate. This method can provide a certain reference for the numerical simulation of unsaturated flow.