Browsing by Author "Taigbenu, A.E."

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    A flux-correct Green element model of quasi three-dimensional multiaquifer flow.
    (American Geophysical Union, 2000-12) Taigbenu, A.E.; Onyejekwe, Okey O.
    Transient flow in multiply layered aquifers, separated by connecting layers of aquitards which provide hydraulic interactions between the aquifers, is solved by the Green element method (GEM) in a manner that reveals one of its strengths of being able to correctly model the leakage flux without resorting to adjusting the grid representing the one-dimensional (l-D) flow in the aquitards, as done in the finite element method (FEM). The hydraulic approach of approximating the flow is adopted so that flow in the aquifer takes place in two dimensions and that in the aquitards takes place in the one-dimensional vertical direction. The 1-D Green element (GE) model earlier developed for transient diffusion and referred to as the transient GE (TGE) formulation [Taigbenu and Onyejekwe, 1999] is used in modeling the flow in the aquitards, while the 2-D GE model developed for linear and nonlinear transient diffusion [Taigbenu and Onyejekwe, 1998] is used for calculating the flows in the confined and unconfined aquifers. Both models are coupled to solve regional flow problems in multiaquifer systems of arbitrary geometry which receive point and distributed recharge of arbitrary strengths. The solution procedure, which is iterative, provides information on the hydraulic heads and fluxes in the aquifers and aquitards at various specified times. Because GEM is founded on the singular integral theory, singularities that arise from water abstractions at wells (point recharge) are naturally captured in the singular Green's function, thereby making it possible to use a more coarse grid for problems in which there exist active wells. Furthermore, the implementation procedure of GEM achieves sparsity of the coefficient matrix so that less amount of computing resources is required for its decomposition. The superiority of the current approach over FEM in predicting the leakage flux through the aquitards and achieving comparable accuracy for well problems with coarser grid is demonstrated
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    A time-dependent Green’s function-based model for stream-unconfined aquifer flows
    (Water research commision, 2004-07-01) Taigbenu, A.E.
    A numerical formulation that is based on the Green element method (GEM), which incorporates a time-dependent Green’s function, is used to solve transient two-dimensional flows of stream-unconfined aquifer interaction. The Green’s function comes from the fundamental solution to the linear diffusion differential operator in two spatial dimensions. In classical boundary element applications, this Green’s function has found use primarily in linear heat transfer and flow problems; its use here for the nonlinear stream-unconfined aquifer flow problem represents the computational flexibility that is achieved with a Green element sense of implementing the singular integral theory. The nonlinear discretised element equations obtained from numerical calculations are linearised by the Picard and Newton-Raphson methods, while the global coefficient matrix, which is banded and sparse, is readily amenable to matrix solution routines. Using four numerical examples, the accuracy of the current formulation is assessed as against an earlier one that incorporates the Logarithmic fundamental solution. It is observed that comparable accuracy is achieved between both formulations, indicating that the current formulation is a viable numerical solution strategy for the stream-aquifer flow problem.