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

Asadi, Roza; Zamani Aliabadi, Zahra

doi:10.61186/NMCE.2302.1007

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

Document Type : Research

Authors

Roza Asadi ¹

Zahra Zamani Aliabadi ²

¹ Assistant professor, Faculty of Civil Engineering, K. N. Toosi University of Technology, Tehran, Iran.

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

10.61186/NMCE.2302.1007

Abstract

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.

Keywords

Numerical modelling

Richards' equation

Unsaturated flow

Finite volume method

Van Genuchten soil model

Subjects

Water Resources Engineering

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