A mass-conservative predictor-corrector solution to the 1D Richards equation with adaptive time control

Abstract

The predictor-corrector-type (P-C) numerical solution to the 1D Richards equation only requires one matrix inversion operation per time step, making it attractive in terms of computational cost. However, the mass conservation could be violated at the saturated-unsaturated interface. A new post-allocation procedure is designed for the P-C method, which redistributes moisture after the corrector step to achieve strict mass balance. A novel adaptive time-stepping strategy is proposed to further improve model efficiency and robustness. It adjusts time step size based on both moisture difference and the Courant number. The proposed solution method and time control strategies are tested and compared with an analytical solution, the previous P-C solution and other existing iterative solutions. The new method shows good conservation property and good agreements to the existing solutions. Compared to the iterative methods that occasionally experience convergence issues, the proposed P-C method is more robust. The new time-control strategy improves computational efficiency compared to the original P-C method, but it remains less efficient than iterative methods for most of the tested scenarios because of its explicit treatment of the corrector step.