1. Specifying Boundary Conditions
Antoine Oliver
Math 1110

2. What are we trying to do?
We are trying to solve our equation for the unknown potential flow 
We need to find  so to do that we have to solve the equation:
2/x + 2/y = 0
Once we have  we can find v by taking the derivatives of 

3. Boundary Conditions
Because we are solving our equations over the Gulf of Mexico we have three boundary conditions that must be accounted for.
Boundaries on land, on the river and on the open sea

4. Boundary Conditions Boundary conditions on land. n  v = 0
Boundary on river .
n • v = -5
Boundary on the open sea.
= 0

5. Specifying Boundary conditions
To specify boundary conditions we need to know which points are open sea, land and rivers
za = z;
z(:,3) = 3; // land
za(77:97,3)=2; //open sea
za(40,3)=1; //river
za(39,3)=1;

6. Plotting the new boundary
Once we have this new matrix we can plot our graph of our new boundary using this code.

7. Code
for n= 1:150
if za(n,3)==3
plot(za(n,2),ymax - za(n,1),'go'); elseif za(n,3)==2
plot(za(n,2),ymax - za(n,1),'bo');
else
plot(za(n,2),ymax - za(n,1),'ro');
hold on;
end

9. Vector Normal Velocity
The vector normal velocity needs to be defined, it will have the same length as za.
normalvelocity = zeros(length(za));
At the points where the river edge will begin it will take the velocity of the river.
normalvelocity(39:40,1) = 5;

10. Calculate Velocity Domain
I want to modify the code of CalculateVelocityDomain such that  = 0 for the nodes on the boundary