Matlab Problem -
Assume you have a 20m*50m rectangular pond. A pollutant enters a 1m*1m rectangular section at the center of pond and initially has the solute concentration of 1000[ML-3], while the solute concentration at other sections of this pond is zero.
At the boundaries the concentration of the pollutant will remain zero. Following the Advection dispersion formula stated below:
∂C/∂t = Dx ∂2C/∂x2 + Dy ∂2C/∂y2
where:
Dx = 1.0, Dy = 0.2
Evaluate and demonstrate using appropriate mathematical tools and graphs how the solute concentration varies in time and how the pollutant is advected and dispersed in this pond.
For solving the above equation use the following discretization methods:
(1) Explicit technique
(2) Crank Nicholson method.
And use iterative techniques (three iterative methods were explained in the class, you may provide results only using Gauss seidel method) for solving your system of linear equations.
And compare your results based on the discretization method you use.
Note that for explicit technique the stability requirement is the following:
Δt (1/Δx2 + 1/Δy2) ≤ 1/2 Δt(1/Δx2 + 1/Δy2) ≤ 1/2
and the Crank Nicholson method is unconditionally stable.
In preparing the report you need to clearly explain your solution algorithm. You also need to specify sections in your code corresponding to each step.
Your graphs need to be analyzed and your results need to be explained clearly.
In the manual report you have to give the mentioned method's (Explicit and Crank Nicholson) at least one trial by explaining procedure and steps solving the problem. And then in the matlab you have to give explanation of each step and in the ouput you have to provide all the graphs tables etc.