Articles | Volume 21, issue 6
Research article
08 Jun 2017
Research article |  | 08 Jun 2017

Ross scheme, Newton–Raphson iterative methods and time-stepping strategies for solving the mixed form of Richards' equation

Fadji Hassane Maina and Philippe Ackerer

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Cited articles

Bause, M. and Knabner, P.: Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods, Adv. Water Resour., 27, 565–581,, 2004.
Belfort, B., Younes, A., Fahs, M., and Lehmann, F.: On equivalent hydraulic conductivity for oscillation–free solutions of Richard's equation, J. Hydrol., 505, 202–217,, 2013.
Bergamaschi, L. and Putti, M.: Mixed finite elements and Newton-type linearizations for the solution of Richards' equation, Int. J. Numer. Methods Eng., 45, 1025–1046,, 1999.
Bouchemella, S., Seridi, A., and Alimi-Ichola, I.: Numerical simulation of water flow in unsaturated soils: comparative study of different forms of Richards's equation, Eur. J. Environ. Civ. Eng. 19, 1–26,, 2015.
Celia, M. A., Bouloutas, E. T., and Zarba, R. L.: A general mass-conservative numerical solution for the unsaturated flow equation, Water Resour. Res., 26, 1483–1496,, 1990.
Short summary
In many fields like climate change, hydrology and agronomy, water movement in unsaturated soils is usually simulated using the Richards equation. However, this equation requires lot of computational effort to be solved due to its highly nonlinear behavior, which hampers its use in simulations. In this paper, we analyze and developed some numerical strategies and we evaluate their reliability and efficiency.