Richards’ equation is often used in unsaturated flow problems

and has a wide range of applications. In the numerical solution

the Richards equation is linearized first

and then the finite difference method is used for numerical discretization and iterative calculation. The traditional iterative methods such as Jacobi iteration

Gauss-Seidel iteration (GS) and SOR iteration have a slower convergence rate

especially when the discrete space step size is small and the discrete time step size is large. Therefore

we adopt the integral correction method and the multistep preconditioner to improve the traditional iterative methods

and propose a improved Gauss-Seidel iterative method with multistep preconditioner based on the integral correction method (ICMP(m)-GS) to solve the linear equations derived from Richards equation. Through examples of unsaturated seepage flow

convergence rate and acceleration effect of the proposed algorithm are validated by comparing the traditional methods and analytical solutions. The results show that the proposed ICMP(m)-GS can greatly improve the ill-condition of linear equations. Compared with the conventional methods GS

SOR and a single improvement method

ICMP(m)-GS has faster convergence rate

higher calculation efficiency and calculation accuracy. This method can serve as a reference for numerical simulation of unsaturated flow.