The full ADE (advection-dispersion equation) in one-dimension, including source/sink terms and simple reactions can be written as:



              dispersion   advection   decay   src/sink   reactions

If retardation is considered we have:

Unlike the ground-water flow equations, one term of the advection-dispersion equation includes a first partial derivative while the other includes a second partial derivative.

The dispersion term is parabolic, while the advection term is hyperbolic. This leads to difficulty in obtaining a numerical solution

ISSUES TO CONSIDER WHEN SOLVING THE ADE INCLUDE Framework, Grid Design, and Solution Scheme:

Approaches to solving the ADE can be divided into Eulerian, Lagrangian, and Mixed Eulerian-Lagrangian methods. They each have advantages and disadvantages.

Global guidance for DESIGNING GRID and TIME STEPS sizes:

When Advection dominates dispersion, designing a model with a small (<2 but sometimes as high as 10 will yield acceptable results) Peclet Number will decrease oscillations, improve accuracy & decrease numerical dispersion.



When Advection dominates dispersion, designing a model with a small (<1) Courant Number, which reflects the portion of a cell that a solute will traverse by advection in one time step, will decrease oscillations, improve accuracy & decrease numerical dispersion.

Solution methods commonly employed for solving the ADE (advection-dispersion equation) include Finite Difference, Finite Elements, Random Walk, and Method of Characteristics. Each has advantages and disadvantages.