Abstract
A new numerical model coupling the modified method of characteristics (MMOC) with the Galerkin finite element method (GFE) is proposed for the assessment of groundwater pollution in regional groundwater flow system. The MMOC-GFE solves governing solute transport equation which involves the simulation of advection and dispersion parts by MMOC and GFE, respectively. This model allows the use of large time steps (large Courant numbers) and large spatial steps (large Peclet numbers) with stable and convergent solutions. The proposed model is successfully implemented for a test case which includes comparison of the model results with reported solutions of other numerical models. It is found that MMOC-GFE model is quite adequate in simulating solute transport in heterogeneous aquifer with combined pumping and injection schemes.
Highlights
Assessment of groundwater pollution using numerical models has the challenge of getting accurate and stable numerical solutions especially in highly heterogeneous media
The proposed modified method of characteristics (MMOC)-Galerkin finite element method (GFE) model in this study attempts to meet this challenge by using Eulerian-Lagrangian formulation
An adaptive Eulerian-Lagrangian formulation (Neuman et al, 1984) solves the advective component of steep concentration front by single step reverse particle tracking of moving particles clustered around each front and the dispersive transport component is solved by Lagrangian formulation on a fixed grid
Summary
Assessment of groundwater pollution using numerical models has the challenge of getting accurate and stable numerical solutions especially in highly heterogeneous media. Garder et al (1964) proposed a method of Kulkarni/ MMOC-GFE Model characteristic technique is for the solution of the solute transport equation which uses imaginary moving particles to represent solute mass and to calculate the concentration change at a given point in the domain for each time step. The method uses single step reverse particle tracking technique for steep concentration fronts and separate weighting factors which relate to grid Peclet and Courant numbers are used for upstream and downstream region of the advection front. Frolkovic (2002) discussed a flux based method of characteristics for simulation of contaminant transport in flowing groundwater This method combines advantages of numerical discretizations by finite volume methods and by methods of characteristics. It is found that the order of the interpolation function has greater effect on solute transport solutions than groundwater flow solutions
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