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United States Department of Agriculture

Agricultural Research Service

Title: Solution of the Nonlinear Transport Equation Using Modified Picard Iteration

Authors
item Huang, Kangle - U.C. RIVERSIDE
item Mohanty, Binayak - U.C. RIVERSIDE
item Leij, Feike - U.C. RIVERSIDE
item Van Genuchten, Martinus

Submitted to: Advances in Water Resources
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: August 20, 1996
Publication Date: N/A

Interpretive Summary: The specter of ground-water contamination looms over many industrialized, suburban, and rural areas. There is a strong demand for quantifying the movement and retention of solutes in the subsurface environment. Numerical models are often used to predict the behavior of contaminants in the subsurface to better protect groundwater resources and plan effective remediation strategies. However, numerically solving the transport problem is often challenged by numerical dispersion and oscillations and frequently ends up with misleading results. Inaccurate results of numerical formulations may be the major cause for many chaos and confusions in the quantitative analyses of solute transport. One of the major problems in solving the transport equation is the mass balance error pertaining to its nonlinear nature when transport involves physical and chemical reactions such as degradation, adsorption, and production. In this paper the mixed-form algorithm of Celia et al. [1990] is generalized to handle the nonlinearity of the transport equation. Numerical experiments are presented to illustrate the advantage of the proposed method over the conventional Picard iteration scheme.

Technical Abstract: The transport and fate of reactive chemicals in groundwater is governed by equations which are often difficult to solve due to the nonlinear relationship between the solute concentrations for the liquid and solid phases. The nonlinearity may cause mass balance errors during the numerical simulations in addition to numerical errors for linear transport system. We have generalized the modified Picard iteration algorithm of Celia et al. [1990] for unsaturated flow to solve the nonlinear transport equation. Numerical results of this mixed-form algorithm are compared with those obtain with the concentration-based scheme using conventional Picard iteration. In general, the new solver resulted in negligible mass balance errors and costed less computational time than the conventional iteration scheme for the test examples, including transport involving highly nonlinear adsorption under steady-state as well as transient flow conditions. In contrast, mass balance errors resulted from the conventional Picard iteration method were higher than 10% for some highly nonlinear problems. Application of the modified Picard iteration scheme to solve the nonlinear transport equation may greatly reduce the mass balance errors and increase computational efficiency.

Last Modified: 11/27/2014
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