TABLE OF CONTENTS

approach / methods

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INTRODUCTION


APPROACH


MINI-EXAMPLES
1-D CLOSED BASIN

2-D DROP IN A BUCKET

 

RESULTS & DISCUSSION

 

CONCLUSIONS

 

REFERENCES


A square, staggered grid was chosen as the mesh for this study.  It was necessary to create a mesh of the site so I took a 2008 aerial image and laid a grid over top of the image, consisting of squares 100 meters X 100 meters.  To cover the study area, it took 4000 squares, which makes sense because the area of the lake is estimated at 40 km2. 

   

Mesh grid of Lake Mendota

Governing Equations

Continuity

Equations of Motion

   (X-dir)

   (Y-dir)

Equations were modified into a finite difference method using a Taylor Series Expansion and dropping off second order terms and higher.

Finite Volume Element

The image to the right shows the finite volume elements used in the model.  The top image shows a top view, where Ui and Uo are velocities in the X direction and Vi and Vo are velocities in the Y direction.  The dot in the middle represents the point where h and eta are considered.

The image in the bottom half is a front view, showing the depth of the element.  h is the initial depth and eta is the change in depth.  The shear stresses are also shown in this image, on the top (usually due to wind) and on the bottom (usually due to bottom friction).

All of this setup was then used to write a program using Matlab®.  After >1000 lines of code, the program was running and I then used it to analyze a few simple cases for testing and then used it to analyze the water levels in the lake over a certain period of time and compared the results to the actual data at the dam.