Saturated-unsaturated groundwater modeling using 3D Richards equation with a coordinate transform of nonorthogonal grids

Baoqing Deng, Junye Wang

Research output: Contribution to journalJournal Articlepeer-review

27 Citations (Scopus)


Saturated-unsaturated flow under a complex terrain is usually solved using the Richards equation. Finite difference or finite volume methods are commonly employed for discretization of Richards equation because of simplicity of coding. Complex subsurface boundary geometries lead to nonorthogonal grids in curvilinear grid systems, which leads to difficulty in discretization and mesh generation. This paper develops a vertical coordinate transform, enabling a computational domain regular in the vertical direction. As a result, the grid of curvilinear surfaces can be successfully transformed to a computational grid that allows solution of the Richards equation with efficient computation and simpler coding. The anisotropic Richards equation in the Cartesian coordinate system is transformed to the equation in the arbitrary coordinate system and further expressed as a form appropriate to the orthogonal coordinate system. The generalized third boundary condition is transformed to a form suited to the orthogonal coordinate system. The finite volume method is used to solve the Richards equation in the orthogonal coordinate system. Four cases are used to validate the present orthogonal coordinate system. The computational results from the orthogonal coordinate system are in good agreement with the results from Ansys Fluent solved in a Cartesian coordinate system for the subsurface flow case. For the coupled case of hill slopes, a good agreement between the computational results and the experimental data is obtained. The present results for V-titled catchment and slab case accord well with the results obtained from HydroGeoSphere and PAWS. The present algorithm can improve grid generation for solution of Richards equation in a hydrological model for a complex domain.

Original languageEnglish
Pages (from-to)39-52
Number of pages14
JournalApplied Mathematical Modelling
Publication statusPublished - Oct. 2017


  • Finite volume method
  • Groundwater modeling
  • Hydrological model
  • Orthogonal coordinate transform
  • Richards equation


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