TY - JOUR

T1 - Saturated-unsaturated groundwater modeling using 3D Richards equation with a coordinate transform of nonorthogonal grids

AU - Deng, Baoqing

AU - Wang, Junye

N1 - Funding Information:
This study was supported by the Alberta Economic Development and Trade for the Campus Alberta Innovates Program (CAIP) Research Chair (No. RCP-12-001-BCAIP). The authors would like to thank the editors and two anonymous reviewers for their constructive comments and suggestions.
Publisher Copyright:
© 2017 Elsevier Inc.

PY - 2017/10

Y1 - 2017/10

N2 - 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.

AB - 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.

KW - Finite volume method

KW - Groundwater modeling

KW - Hydrological model

KW - Orthogonal coordinate transform

KW - Richards equation

UR - http://www.scopus.com/inward/record.url?scp=85028020320&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2017.05.021

DO - 10.1016/j.apm.2017.05.021

M3 - Journal Article

AN - SCOPUS:85028020320

SN - 0307-904X

VL - 50

SP - 39

EP - 52

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

ER -