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WRRCTMR No.84 The Cell-Analytical-Numerical Technique for Solving Unsaturated-Flow and Solute-Transport Problems

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Title: WRRCTMR No.84 The Cell-Analytical-Numerical Technique for Solving Unsaturated-Flow and Solute-Transport Problems
Authors: El-Kadi, Aly I.
Elnawawy, Osman A.
Keywords: solute transport
unsaturated flow
soil water
finite element method
cell analytical-numerical method
show 3 morewater flow
soil moisture flux
solute mass flux

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LC Subject Headings: Fluids -- Migration -- Mathematical models.
Groundwater flow -- Mathematical models.
Soils -- Solute movement -- Mathematical models.
Issue Date: Mar 1992
Publisher: Water Resources Research Center, University of Hawaii at Manoa
Citation: El-Kadi AI, Elnawawy OA. 1992. The cell-analytical-numerical technique for solving unsaturated-flow and solute-transport problems. Honolulu (HI): Water Resources Research Center, University of Hawaii at Manoa. WRRC technical memorandum report, 84.
Series/Report no.: WRRC Technical Memorandum Reports
Abstract: The cell analytical-numerical (CAN) method was developed and applied for the solution of one dimensional water flow and solute transport problems in the unsaturated zone. The flow equation is characterized by a nonlinear governing equation. The CAN method is similar to other numerical techniques in that it divides the domain into a number of computational elements, each homogeneous in nature. It differs, however, by implementing a local analytical solution within the element. The soil moisture flux (for the flow equation) or solute mass flux (for the transport equation) is applied at the interface between two adjacent elements to define an algebraic relationship between the values of pressure head or concentration, respectively, at three neighboring points. Assembling these three-point equations provides a tridiagonal system of equations that can be solved by the Thomas algorithm. The system describing the flow problem is nonlinear in nature, and is solved iteratively within an implicit linearization scheme. For water flow, the method is applied to a number of soil types and the results are compared to Philip's semi-analytical solution and a numerical solution that is based on the finite-element
technique. The results indicate the method's high accuracy over a wide range of soil types. However, an upstream weighting approach is needed for coarser soils, a process that may lead to relatively large mass-balance errors. The high accuracy of the solute transport solutions is demonstrated through comparison against available analytical solutions.
Sponsor: U.S. Department of the Interior, Geological Survey Grant/Contract No. 14-08-0001-G1558-02
Pages/Duration: viii + 21 pages
Appears in Collections:WRRC Technical Memorandum Reports

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