Numerical simulation of general hydrodynamic dispersion in porous medium

dc.contributor.authorNalluswami, Marappagounder, author
dc.contributor.authorLongenbaugh, R. A., advisor
dc.descriptionAugust 1971.
dc.descriptionIncludes bibliographic references (pages 84-88).
dc.description.abstractA general two-dimensional equation of dispersion in a porous medium is presented. The second order linear partial differential equation describing the transient concentration distribution has mixed partial derivatives which is the result of treating the dispersion coefficients as second order symmetric tensors. Using the principles of calculus of variations a "functional" is developed for the dispersion equation that has mixed partial derivatives. The two-dimensional region is divided into triangular finite elements of arbitrary size and shape. The concentration is assumed to vary linearly over each triangular finite element. Minimization of the functional in combination with the finite element method leads to a system of simultaneous, first order, linear, ordinary differential equations. The matrix differential equation is numerically integrated using the fourth order Runge-Kutta and Adams-Moulton multistep predictor-corrector methods. Before proceeding with the use of the new functional, solutions were obtained for the dispersion equation with mixed partial derivatives in a rotated coordinate system. The numerical solutions using the new functional for one- and two-dimensional problems compared favourably with the available analytic solutions and the results obtained by finite element method that use a different functional. It was shown that the new functional can handle different ratios of lateral to longitudinal dispersion. A general stability criteria for the resulting matrix equation is developed. Stability dependent on the data is discussed in detail with examples. A brief description of the numerical instability is also given.
dc.format.mediumdoctoral dissertations
dc.publisherColorado State University. Libraries
dc.relationCatalog record number (MMS ID): 991004373289703361
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dc.subject.lcshDiffusion in hydrology -- Mathematical models
dc.subject.lcshPorosity -- Mathematical models
dc.subject.lcshGroundwater -- Pollution -- Mathematical models
dc.titleNumerical simulation of general hydrodynamic dispersion in porous medium
dcterms.rights.dplaThis Item is protected by copyright and/or related rights ( 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). Engineering State University of Philosophy (Ph.D)
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