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United States Department of Agriculture

Agricultural Research Service

Title: A Third-Order Numerical Scheme with Upwind Weighting for Solving the Solute Transport Equation

Authors
item Huang, Kangle - U.C. RIVERSIDE
item Simunek, Jirka - U.C. RIVERSIDE
item Van Genuchten, Martinus

Submitted to: International Journal for Numerical Methods in Engineering
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: March 12, 1997
Publication Date: N/A

Interpretive Summary: The quality of groundwater depends upon the quality of water infiltrating the vadose zone and the ensuing physical, chemical and biological reactions and transformations involving this water and its dissolved solutes as they move through the unsaturated zone toward the groundwater table. Solute transport in variably-saturated soils and groundwater is generally described using convection-dispersion type transport equations. Especially challenging has been the formulation of numerical solutions that are free of oscillations and artificial dispersion The objective of this paper is to develop a numerical solution method for the variably-saturated solute transport equation which is not only free of numerical oscillations, but also produces no or limited numerical dispersion. The objective is achieved by first extending the dispersion- corrected numerical scheme of van Genuchten and Gray (1978) to transport under transient variably-saturated flow conditions and nonlinear adsorption. Subsequently, the derived third-order approximation of the transport equation will be solved using the upwind Petrov/Galerkin finite element method.

Technical Abstract: Solute transport in the subsurface is generally described quantitatively with the convection-dispersion transport equation. Accurate numerical solutions of this equation are important to ensure physically realistic predictions of contaminant transport in a variety of applications. An accurate third-order in time numerical approximation of the solute transport equation was derived. The approach leads to corrections for both the dispersion coefficient and the convective velocity when used in numerical solutions of the transport equation. The developed algorithm is an extension of previous work to solute transport conditions involving transient variably-saturated fluid flow and nonlinear adsorption. The third-order algorithm is shown to yield very accurately solutions near sharp concentration fronts, thereby showings its ability to eliminate numerical dispersion. However, the scheme does suffer from numerical oscillations. The oscillations could be avoided by employing upwind weighting techniques in the numerical scheme. Solutions obtained with the proposed method were free of numerical oscillations and exhibited negligible numerical dispersion. Results for several examples, including those involving highly nonlinear sorption and infiltration into initially d soils, were found to be very accurate when compared to other solutions.

Last Modified: 8/31/2014
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