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oai:mountainscholar.org:10217/2445892026-05-22T17:17:45Zcom_10217_100532com_10217_100000com_10217_100369com_10217_100303col_10217_100538col_10217_100381

Al-Dhamari, Mohamed Ali Dhbeel, author Warner, James A., advisor Fontaine, Darrell G., committee member Sanford, William E., committee member Afifi, Sameh M., committee member 2026-05-19T18:02:48Z 2002 https://hdl.handle.net/10217/244589 https://doi.org/10.25675/3.027038 A new numerical methodology for solving the partial differential equation governing the unsaturated flow of water in porous media is developed and applied to approximate the hydraulic head and to solve for the flux functions that obey the one-dimensional unsaturated flow equation. The algorithms are based on a Fourier finite element type of formulation, which combines the efficiency of the Fourier series expansion as a refinement tool and the finite element method, where the spatial domain is divided into discrete elements and nodal points. A truncated Fourier series expansion was used as the approximating function over orthogonal discrete elements. The Fourier cosine series was selected for the expansion series and the same denomination is used for the numerical integration techniques using polynomials of a high order as approximating functions. The solution to the partial differential equation is obtained by marching through time in discrete steps, beginning with a known solution of Fourier series coefficients at time zero. A Fourier finite element computer program based on the new methodology was written and applied to modeling a one-dimensional flow of water into porous media. The nonlinear solution behavior was well simulated by the high order approximating functions. The accuracy of the numerical solution used in this model was evaluated by analyzing a test problem for which the solution is available, and a good agreement was obtained. doctoral dissertations English eng Colorado State University. Libraries 2000-2019 Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. Per the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users. civil engineering A Fourier finite element model for unsaturated flow in porous media Text Doctor of Philosophy (Ph.D.) Doctoral Civil Engineering Colorado State University This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). open.access