The Cell Analytic-Numerical Method for Solution of the Groundwater Solute Transport Equation

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Elnawawy, Osman Ali

Contributors dc:contributor

• Valocchi, Albert J.

• Engineering, Civil

Identifier

(UMI)AAI8908671

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/69983