Comparison of numerical methods for the solution of Richards' equation in layered porous media

Document Type : Research


1 Civil Engineering Department , K.N. Toosi University of Technology, Tehran, Iran

2 M.Sc. student, K. N. Toosi University of Technology, Tehran, Iran.


In this research, the advanced finite volume scheme of the Dual Discrete method has been used for the numerical modeling of Richards' equation. Three forms of Richards' equation, including head form, water content form, and mixed form with a modified Picard linearization, are developed and assessed in the two-dimensional domain. Various examples using different soil properties, boundary conditions, and grid structures are solved. The results agree very well with the analytical and numerical solutions in both homogenous and layered porous media. The different forms have been compared in terms of accuracy, the number of iterations, and mass balance ratio. For the test cases considered in this study, the water content form has been determined as the superior method due to the low mass balance error, higher accuracy, and less number of iterations. Also, the modified Picard form improves the conservation of mass and efficiency in comparison to the head-based method. The results indicate that for the head form, a small time step is required to obtain an accurate mass balance, while the two other schemes yield superior mass balance results, even for large time steps. Moreover, the proposed finite volume method shows stable solutions without any numerical oscillations for all of the test cases.


Main Subjects

Articles in Press, Accepted Manuscript
Available Online from 13 July 2023
  • Receive Date: 26 February 2023
  • Revise Date: 04 July 2023
  • Accept Date: 10 July 2023