A Retrospective Temporal Integration Method for Richards' Equation

Numerical simulation is the effective method of solving Richards’ equation for whose highly-nonlinear character. Most methods of the numerical solutions improved the special discrete methods, or designed on the basis of physical conservation. Those methods can be solved when one time initial value is given. Combining the self-memory principle, the retrospective time integration method for Richards’ equation is proposed. It is a new kind of time integration scheme which could include multi-time historical data, absorbs the character of stochastic method which forecast by making use of multi-time historical data before the initial time. This scheme is applied to simulate the fixed head vertical infiltration. The results of 1-order retrospective scheme are calculated with given memory coefficients. The stable region of the memory coefficients in 1-order retrospective scheme is also given. The results show that the retrospective scheme can get higher accuracy than the implicit scheme.