Modelling Unsaturated Flow in Porous Media Using an Improved Picard Iteration Scheme

The numerical solution of various systems of linear equations describing fluid infiltration uses the Picard iteration (PI). However, because many such systems are ill-conditioned, the solution process often has a poor convergence rate, making it very time-consuming. In this study, a control volume method based on non-uniform nodes is used to discretize the Richards equation, and adaptive relaxation is combined with a multistep preconditioner to improve the convergence rate of PI. The resulting adaptive relaxed PI with multistep preconditioner (MP( m )-ARPI) is used to simulate unsaturated flow in porous media. Three examples are used to verify the proposed schemes. The results show that MP( m )-ARPI can effectively reduce the condition number of the coefficient matrix for the system of linear equations. Compared with conventional PI, MP( m )-ARPI achieves faster convergence, higher computational efficiency, and enhanced robustness. These results demonstrate that improved scheme is an excellent prospect for simulating unsaturated flow in porous media.