Project

Introduction

The project will be assigned after I learn more about the abilities of the individual students in the class. Normally, the project is defined in a sentence or a short paragraph (e.g., the 2004 project)..

Once the project is defined, you need to

• Pick a mathematical model
• Pick a discretization method
• Write a quick, simple code in Matlab
• If there is time, write a parallel code for use in the CSLab using MPI in C or Fortran. OpenMP is also an option if you can find a parallel resource that has it already installed.
• Visualize the calculation.

Obviously, you would need a long time to do this at a professional level. You do not have the needed time, so you will have to take a number of shortcuts.

In the end, the class (as a group) should turn in

• A report (cf., Sports Lighting project) detailing what you did, the choices, why you made the choices you did, and numerical results. An appendix with a table describing who did what is mandatory.
• Working codes (Matlab,  C, C++, Fortran, Python, etc.)

Good luck.

Project Description

You have a low level of concentration of a pollutant in a lake. The lake is connected to just one river, providing the pollutant infrequently from a source upstream. By coincidence, the lake can be considered a unit square, the rivers are at the upper left corner (the source) and lower right corner (the sink), and the velocity of the river is a uniform v=(1,0). The velocity of the river must be a vector since the problem is two dimensional. There are four sensors in the lake that provide data on a regular basis, except when a sensor fails to successfully transmit data to the collecting agent. Your project is to model the concentration of the pollutant in the lake based on the sensor data. You can make predictions when the concentration is well known, but you have to recompute the concentration in the entire lake when new material is discovered by the sensors.

The lake and river configuration looks like

______________________________
___                                                      |
      |                                              S     |
      |              S                                     |
      |                                                     |
      |                                                     |
      |                                                     |
      |                                      S             |
      |         S                                          |
      |                                                     |___
      |______________________________

The river is not part of domain.

If this problem is too hard, reduce the problem to a river, which can be thought of as a straight line with sensors at several points. It is essential that you have more than one sensor, however.

I will provide data for the sensors once you have enough of a program devised to use the data. It will depend on whether you are running in 2D or 1D. You should assume a concentration level of 0.01 uniformly as an initial guess. The river is small, say 5% of the left or right side of the lake.