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Comparison of ELLAM and LEZOOMPC for Developing an Efficient Modeling Technique  

Suk Hee-Jun (Korea Water Resources Corporation, Korea Institute of Water and Environment)
Publication Information
Journal of Soil and Groundwater Environment / v.11, no.1, 2006 , pp. 37-44 More about this Journal
Abstract
This study summarizes advantages and disadvantages of numerical methods and compares ELLAM and LEZOOMPC to develop an efficient numerical modeling technique on contaminant transport. Eulerian-Lagrangian method and Eulerian method are commonly used numerical techniques. However Eulerian-Lagrangian method does not conserve mass globally and fails to treat boundary in a straightforward manner. Also, Eulerian method has restrictions on the size of Courant number and mesh Peclet number because of time truncation error. ELLAM (Eulerian Lagrangian Localized Adjoint Method) which has been popularly used for past 10 years in numerical modeling, is known for overcoming these numerical problems of Eulerian-Lagrangian method and Eulerian method. However, this study investigates advantages and disadvantages of ELLAM and suggests a change for the better. To figure out the disadvantages of ELLAM, the results of ELLAM, LEZOOMPC (Lagrangian-Eulerian ZOOMing Peak and valley Capturing), and visual MODFLOW are compared for four examples having different mesh Peclet numbers. The result of ELLAM generates numerical oscillation at infinite of mesh Peclet number, but that of LEZOOMPC yields accurate simulations. The simulation results suggest that the numerical error of ELLAM could be alleviated by adopting some schemes in LEZOOMPC. In other words, the numerical model which combines ELLAM with backward particle tracking, forward particle tracking, adaptively local zooming, and peak/valley capturing of LEZOOMPC can be developed for not only overcoming the numerical error of ELLAM, but also keeping the numerical advantage of ELLAM.
Keywords
ELLAM; LEZOOMPC; Local zooming; Peak/valley capturing;
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1 Baptista, A.M., Adams, E., and Stolzenbach, K., 1984, Eulerian-Lagrangian analysis of pollutant transport in shallow water, Rep. 296, R.M. Parsons Lab. for Water Resour. and Hydrodyn., Mass. Inst. of Technol., Cambridge
2 Celia, M.A., 1994, Eulerian-Lagrangian localized adjoint methods for contaminant transport simulations, In Computational Methods in Water Resources X, ed. Alexander Peters et al. Kluwer Academic Press, London, 207-216
3 Douglas, J. and Russell, T.F., 1982, Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal., 19,871-885   DOI   ScienceOn
4 Healy, R. W. and Russell, T.F., 1998, Solution of the advectiondispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method, Adv. Water Resour., 21(1), 11-26   DOI   ScienceOn
5 Konikow, L.F. and Bredehoeft, J.D., 1978, Computer model of two-dimensional solute transport and dispersion in groundwater, Techniques of Water-Resources Investigation of the United Sates Geological Survey, chapter C2, book 7, USGS, Reston, Va
6 Leonard, B.P. and Mokhtari, S., 1990, Beyond first-order unwinding: The ULTRA-SHARP alternative for non-oscillatory steady-state simulation of convection, lnt. J. Numer. Methods Eng., 30, 729-866   DOI
7 Russell, T.F., 1990, Eulerian-Lagrangian localized adjoint methods for advection-dominated problems. In Numerical Analysis, 1989, Pitman Res. Notes Math, Series, Vol. 228, ed. D.F. Griffiths & G.A. Watson. Longman Scientific and Technical, Harlow, U.K., 206-228
8 Celia, M.A., Russell, T.F., Herrera, I., and Ewing, R.E., 1990, An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation, Adv. Water Resour., 13, 187-206   DOI   ScienceOn
9 Healy, R.W. and Russell, T.F., 1993, A finite-volume Eulerian-Lagrangian localized adjoint method for solution of the advection-dispersion equation, Water Resow: Res., 29, 2399-2413   DOI   ScienceOn
10 Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, M.G., 2000, MODFLOW-2000, The U.S. Geological Survey modular ground water model-User guide to modularization concepts and the ground water flow process, Open-File Report 00-92, US Geological Survey
11 Yeh, G.T., 1990, A Lagrangian-Eulerian method with zoomable hidden fine-mesh approach to solving advection-dispersion equations, Water Resour. Res., 26(6), 1133-1144   DOI
12 Herrera, I., Ewing, R.E., Celia, M.A., and Russell, T.F., 1993, Eulerian-Lagrangian localized adjoint methods: the theoretical framework, Numer. Meth. PDEs, 9, 431-458   DOI
13 Baptista, A.M., 1987, Solution of advection-dominated transport by Eulerian-Lagrangian methods using the backward methods of characteristics, Ph.D. thesis, Dep. of Civ. Eng., Mass. Inst. of Technol., Cambridge
14 Cheng, J.R., Cheng, H.P., and Yeh, G.T., 1996, A Lagrangian-Eulerian method with adaptively local zooming and peak/valley capturing approach to solve two-dimensional advection-diffusion transport equations, International J. Numerical Methods in Engineering, 39, 987-1016   DOI
15 Yeh, G.T., Chang, J.R., and Short, T.E., 1992, An exact peak capturing and oscillation-free scheme to solve advection-dispersion transport equations, Water Resour. Res., 28(11), 2937-2951   DOI   ScienceOn
16 Leonard, B.P., 1988, Universal limiter for transient interpolation modeling of advective transport equations: The ULTIMATE conservative difference scheme, NASA Tech. Memo. 100916
17 Binning, P.J. and Celia, M.A., 1996, A finite volume Eulerian-Lagrangian localized adjoint method for solution of contaminant transport equations in two-dimensional multi phase flow systems, Water Resour. Res., 32, 103-114   DOI
18 Williamson, D.L., and Rasch, P.J., 1988, Two-dimensional semi-Lagrangian transport with shape preserving interpolation, Mon. Weather Rev., 117, 102-109   DOI