Journal
ADVANCES IN WATER RESOURCES
Volume 148, Issue -, Pages -Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.advwatres.2020.103841
Keywords
Richards equation; Linearization schemes; Numerical convergence analysis; Second-order time-accuracy; Galerkin finite elements; Mixed finite elements
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Funding
- UM6P/OCP group of Morocco
- Natural Sciences and Engineering Research Council of Canada [RGPIN2019-06855]
- UM6P/OCP group of Morocco [UM6P-OCP-IWRI-2019]
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This study analyzes different weak formulations and computational techniques for efficiently solving the Richards equation, with a focus on semi-implicit schemes as a good alternative when implicit schemes encounter convergence issues. The developed scheme, based on proposed temporal extrapolation techniques and the mixed formulation, outperforms other schemes in numerical convergence studies and tests.
This study concerns numerical methods for efficiently solving the Richards equation where different weak formulations and computational techniques are analyzed. The spatial discretizations are based on standard or mixed finite element methods. Different implicit and semi-implicit temporal discretization techniques of second-order accuracy are studied. To obtain a linear system for the semi-implicit schemes, we propose second-order techniques using extrapolation formulas and/or semi-implicit Taylor approximations for the temporal discretization of nonlinear terms. A numerical convergence study and a series of numerical tests are performed to analyze efficiency and robustness of the different schemes. The developed scheme, based on the proposed temporal extrapolation techniques and the mixed formulation involving the saturation and pressure head and using the standard linear Lagrange element, performs better than other schemes based on the saturation and the flux and using the Raviart-Thomas elements. The proposed semi-implicit scheme is a good alternative when implicit schemes meet convergence issues.
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