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A THIRD‐ORDER NUMERICAL SCHEME WITH UPWIND WEIGHTING FOR SOLVING THE SOLUTE TRANSPORT EQUATION
Author(s) -
HUANG KANGLE,
ŠIMŮNEK JIŘÍ,
VAN GENUCHTEN M. TH.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970515)40:9<1623::aid-nme131>3.0.co;2-v
Subject(s) - convection–diffusion equation , weighting , mechanics , upwind scheme , dispersion (optics) , numerical analysis , convection , computer simulation , mathematics , mathematical analysis , physics , discretization , optics , acoustics
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 non‐linear adsorption. The third‐order algorithm is shown to yield very accurately solutions near sharp concentration fronts, thereby showing 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 non‐linear sorption and infiltration into initially dry soils, were found to be very accurate when compared to other solutions. © 1997 by John Wiley & Sons, Ltd.