Articles | Volume 16, issue 2
Development and technical paper
27 Jan 2023
Development and technical paper |  | 27 Jan 2023

A simple, efficient, mass-conservative approach to solving Richards' equation (openRE, v1.0)

Andrew M. Ireson, Raymond J. Spiteri, Martyn P. Clark, and Simon A. Mathias

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Cited articles

Bear, J. and Cheng, A. H. D.: Modeling groundwater flow and contaminant transport, Vol. 23, in: Theory and Applications of Transport in Porous Media, Springer, Dordrecht, 834,, 2010. 
Beven, K., and Germann, P.: Macropores and water flow in soils revisited, Water Resour. Res., 49, 3071–3092,, 2013. 
Brown, P. N., Hindmarsh, A. C., and Byrne, G. D.: VODE. Variable Coefficient ODE Solver, SIAM J. Sci. Stat. Comp., 10, 1038–1051,, 1989. 
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. 
Clark, M. P., Fan, Y., Lawrence, D. M., Adam, J. C., Bolster, D., Gochis, D. J., Hooper, R. P., Kumar, M., Leung, L. R., Mackay, D. S., and Maxwell, R. M.: Improving the representation of hydrologic processes in Earth System Models, Water Resour. Res., 51, 5929–5956, 2015. 
Short summary
Richards' equation (RE) is used to describe the movement and storage of water in a soil profile and is a component of many hydrological and earth-system models. Solving RE numerically is challenging due to the non-linearities in the properties. Here, we present a simple but effective and mass-conservative solution to solving RE, which is ideal for teaching/learning purposes but also useful in prototype models that are used to explore alternative process representations.