Several noniterative procedures for solving the nonlinear Richards equation are introduced and compared to the conventional Newton and Picard iteration methods. Noniterative strategies for the numerical solution of transient, nonlinear equations arise from explicit or linear time discretizations, or they can be obtained by linearizing an implicit differencing scheme. We present two first order accurate linearization methods, a second order accurate two-level "implicit factored" scheme, and a second order accurate three-level "Lees" method. The accuracy and computational efficiency of these four schemes and of the Newton and Picard methods are evaluated for a series of test problems simulating one-dimensional flow processes in unsaturated porous media. The results indicate that first order accurate schemes are inefficient compared to second order accurate methods; that second order accurate noniterative schemes can be quite competitive with the iterative Newton and Picard methods; and that the Newton scheme is no less efficient than the Picard method, and for strongly nonlinear problems can outperform the Picard scheme. The two second order accurate noniterative schemes appear to be attractive alternatives to the iterative methods, although there are concerns regarding the stability behavior of the three-level scheme which need to be resolved. We conclude that of the four noniterative strategies presented, the implicit factored scheme is the most promising, and we suggest improved formulations of the method. linear discretizations and linearization procedures which allow us to avoid iterations in the numerical solution of Richards' equation.The simplest approach for solving the nonlinear Richards equation numerically is to use an explicit two-level time discretization. This approach yields a linear system of equations, minimizes storage requirements, and on a per time step basis it represents a least cost option. However, stability constraints for explicit methods are quite stringent, and therefore for long simulations or for problems which require fine spatial resolution (such as infiltration involving a steep moisture front), the small time step sizes required to main-Paper number 91 WR00334. 0043-1397/91/91 WR-00334505.00 tain a stable solution can render these schemes very costly on a per simulation basis. In general, therefore, unconditionally stable implicit time discretizations have been utilized to solve the Richards equation numerically. The weighted two-level implicit discretization most commonly used results in a nonlinear system of equations, and the conventional approach has been to solve this nonlinear system using an iterative procedure. The most widely used iterative techniques are the Newton (also known as Newton-Raphson) and Picard methods, with the simpler Picard method being the more popular of the two [CooleyAlthough we find that the Newton and (to a lesser extent) the Picard schemes are generally robust, these iterative methods entail computational costs associated with having to evaluate and...

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