A NEW CONVERGENCE CRITERION FOR THE MODIFIED PICARD ITERATION METHOD TO SOLVE THE VARIABLY SATURATED FLOW EQUATION

Solutions of the Richards equation for wafer flow in variably saturate d porous media are increasingly being used in water resources evaluati on and environmental management. Besides the accuracy of solution, als o of concern is the required computational effort, especially when hig hly nonlinear soil hydraulic properties and dry initial conditions are involved. In this paper we evaluate the performance of different conv ergence criteria when the modified Picard iteration method is used for solving the mixed-form Richards equation. Results are compared in ter ms of computer processing (CPU) time and number of iterations. A new n onlinear convergence criterion derived using a Taylor series expansion of the water content was implemented in the mixed-form numerical algo rithm. The computational efficiency of the new criterion was evaluated against two widely used convergence criteria for different soil types , boundary conditions, initial conditions, and layered soils. Whereas all three criteria produced nearly identical results in terms of calcu lated water content, pressure head, and water flux distributions, all with negligible mass balance errors, the required CPU times were signi ficantly different. In general, the new nonlinear convergence criterio n was found to be computationally much more efficient than the other t wo criteria. The new criterion was also more robust (i.e. the solution remained convergent) fdr highly nonlinear flow problems for which the other two convergence criteria failed. Results of this study indicate that the new convergence criterion, when implemented in the modified Picard solution of the mixed-form Richards equation, produces a very e fficient and accurate method for simulating variably saturated water f low in soils.