An improved method for inhomogeneous space grid in the simulation of unsaturated flow

Abstract

The Richards’ equation is widely used in the simulation of unsaturated flow and related fields. In the numerical solution process, the finite difference method can be used to carry out numerical discretization and iterative calculation. However, in order to obtain a more reliable numerical solution, the space step size of a conventional uniform grid is often small. For some unfavorable numerical conditions, such as infiltration into dry soil, iterative calculation is time-consuming and even the accuracy cannot be improved very well. Therefore, an improved method is proposed by using the Chebyshev space grid, which combines the finite difference method to numerically discretize the Richards’ equation to obtain linear equations. Then the classic Picard iterative method is used to iteratively solve the linear equations to obtain the numerical solutions of the Richards’ equations. Through two examples of unsaturated flow under unfavorable conditions for homogeneous soil and layered soil, combined with the analytical solution of the model and the software Hydrus-1D, the accuracy of the numerical solution obtained by the improved grid method and the uniform grid method is compared and examined. The results show that the proposed Chebyshev grid method can obtain higher numerical accuracy with a smaller number of nodes than the traditional uniform grid, and the computational cost is smaller. This method has a good application prospect.

Keywords

• richards’ equation
• finite difference
• uniform grid
• chebyshev grid
• numerical accuracy