The Cell Analytic-Numerical Method for Solution of the Groundwater Solute Transport Equation
Elnawawy, Osman Ali
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https://hdl.handle.net/2142/69983
Description
Title
The Cell Analytic-Numerical Method for Solution of the Groundwater Solute Transport Equation
Author(s)
Elnawawy, Osman Ali
Issue Date
1988
Doctoral Committee Chair(s)
Valocchi, Albert J.
Department of Study
Civil Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Abstract
A new numerical scheme called the Cell Analytic-Numerical (CAN) method for the efficient solution of groundwater solute transport problems is developed and evaluated. The basic idea of the CAN method is the incorporation of local analytic solutions into the numerical solution of the partial differential equation. The CAN method decomposes the entire solution domain into a number of rectangular cells (volume subdomains). Also, each cell is homogeneous so that a local analytic solution to the solute transport equation can be obtained. Finding the local analytical solution is facilitated by approximating the time derivative via a first order accurate forward finite difference quotient and by using a transverse averaging procedure (i.e., integration over all but one of the spatial variables), through which the governing partial differential equation is transformed into a set of coupled one-dimensional ordinary differential equations for the concentration moments. This set of equations is solved analytically in terms of "source-like" expressions (the approximated time derivative along with the resulting integrated-terms evaluated at the cell surfaces of the non-integrated direction). The solute mass flux continuity across cell surfaces is then used, along with the local analytical solution, to construct an algebraic relationship between the concentration moment values at adjacent cell surfaces. Assembling all the cells together results in a set of coupled tridiagonal matrix equations, one set for each spatial direction, which can be solved very efficiently.
A series of test problems is used to demonstrate the one-, two-, and three-dimensional computational capabilities of the Cell Analytic-Numerical method. The results are compared to analytical solutions and to those obtained using the finite difference and finite element methods. For large spatial grid sizes, the CAN method is shown to yield a significant increase in the accuracy relative to the other methods tested. The stability of the CAN method is investigated through the well-known von Neumann procedure. The analysis indicates that the CAN method is unconditionally stable.
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