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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Veröffentlicht in:	Transport in porous media Jg. 91; H. 1; S. 35 - 47
Hauptverfasser:	Juncu, Gheorghe, Nicola, Aurelian, Popa, Constantin
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Dordrecht Springer Netherlands 01.01.2012 Springer Springer Nature B.V
Schlagworte:	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
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Abstract	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.
AbstractList	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.
Author	Juncu, Gheorghe Popa, Constantin Nicola, Aurelian
Author_xml	– sequence: 1 givenname: Gheorghe surname: Juncu fullname: Juncu, Gheorghe email: juncugh@netscape.net, juncu@easynet.ro organization: Politehnica University Bucharest – sequence: 2 givenname: Aurelian surname: Nicola fullname: Nicola, Aurelian organization: Department of Mathematics, Ovidius University – sequence: 3 givenname: Constantin surname: Popa fullname: Popa, Constantin organization: Department of Mathematics, Ovidius University
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Cites_doi	10.1002/(SICI)1097-0207(19990720)45:8<1025::AID-NME615>3.0.CO;2-G 10.1090/S0025-5718-1977-0431719-X 10.1029/1999WR900349 10.1016/j.advwatres.2005.12.011 10.1016/j.advwatres.2005.06.007 10.1137/100786320 10.3934/dcdsb.2010.13.435 10.1023/A:1011562522244 10.1002/nme.1481 10.1023/A:1006555107450 10.1137/0907058 10.1016/j.advwatres.2004.03.005 10.1016/S0378-4754(00)00143-9 10.1002/fld.1369 10.1155/AAA.2005.813 10.1002/fld.1087 10.2136/sssaj1977.03615995004100020024x 10.2136/vzj2007.0077 10.1016/j.jhydrol.2005.01.019 10.1029/94WR03291 10.2136/vzj2005.0005 10.1137/0910004 10.1016/j.ijheatmasstransfer.2006.11.005 10.1016/S0309-1708(98)00057-8 10.1137/0913035 10.1007/s11242-009-9465-3 10.1029/WR023i004p00542 10.1029/WM015 10.1016/j.jhydrol.2010.09.004 10.1080/01630560802418078 10.1029/2008WR007654 10.1016/0021-9991(81)90041-3 10.1016/j.apnum.2005.06.007 10.1007/s11242-007-9180-x 10.1016/j.cma.2008.06.005 10.1002/fld.74 10.2136/sssaj1980.03615995004400050002x 10.1111/j.1365-2389.2007.00972.x 10.1007/978-3-662-02427-0 10.1002/cnm.1364 10.2136/vzj2004.1031 10.1007/978-94-011-2632-8
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Keywords	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
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SubjectTerms	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
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Title	Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions
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