Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

The need of accurate and efficient numerical schemes to solve Richards’ equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards’ equation modeling water flow in variably satur...

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Bibliographic Details
Published in:Transport in porous media Vol. 91; no. 1; pp. 35 - 47
Main Authors: Juncu, Gheorghe, Nicola, Aurelian, Popa, Constantin
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.01.2012
Springer
Springer Nature B.V
Subjects:
Civil Engineering
Classical and Continuum Physics
Computer simulation
Discretization
Earth and Environmental Science
Earth Sciences
Earth, ocean, space
Exact sciences and technology
Finite volume method
Flow equations
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Hydrology. Hydrogeology
Hydrology/Water Resources
Industrial Chemistry/Chemical Engineering
Infiltration
Multigrid methods
Numerical methods
Porous media
Saturated soils
Soil properties
Two dimensional models
Unsaturated soils
Water flow
Saturated–unsaturated porous media
Richards’ equation
Finite volume
Nonlinear multigrid algorithm
algorithms
models
ground water
Finite volume method
transport
Richards equation
infiltration
unsaturated zone
hydraulics
solution
Saturated-unsaturated porous media
saturated zone
soils
porous media
methodology
Richards' equation
ISSN:0169-3913, 1573-1634
Online Access:Get full text
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Summary:The need of accurate and efficient numerical schemes to solve Richards’ equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards’ equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems simulate infiltration of water in 2D saturated–unsaturated soils with hydraulic properties described by van Genuchten–Mualem models. The numerical results obtained are compared with those provided by the modified Picard–preconditioned conjugated gradient (Krylov subspace) approach.
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ISSN:0169-3913
1573-1634
DOI:10.1007/s11242-011-9831-9