• Journal of Soil and Groundwater Environment
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• v.11 no.1
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• pp.37-44
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• 2006

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.

• Journal of Korea Soil Environment Society
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• v.5 no.1
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• pp.3-12
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• 2000

The multi-region model, to describe preferential flow, is an equation representing solute transport in soils by dividing soil into numerous pore groups and using the hydraulic properties of the soil. As the model partial differential equation (PDE) is solved numerically with finite difference methods. a modified equivalent partial differential equation(MEPDE) of the partial differential equation of the multi-region model is derived to analyze the accuracy and consistency of the solution of the model PDE and the Von Neumann method is used to analyze the stability of the finite difference scheme. The evaluation obtained from the MEPDE indicated that the finite difference scheme was found to be consistent with the model PDE and had the second order accuracy The stability analysis is performed to analyze the model PDE with the amplification ratio and the phase lag using the Von Neumann method. The amplification ratio of the finite difference scheme gave non-dissipative results with various Peclet numbers and yielded the most high values as the Peclet number was one. The phase lag showed that the frequency component of the finite difference scheme lagged the true solution. From the result of the stability analysis for the model PDE, it is analyzed that the model domain should be discretized in the range of Pe < 1.0 and Cr < 2.0 to obtain the more accurate solution.