I've figured this out and I'm going to answer my own question.
Rather than find the unit normal for the point, it is easier to find the equation for the "curve" of interest. In the diagram I attached, I could take 3 points two either side of where I have annotated the normal. From the location...
Homework Statement
I am using the boundary element method to solve unknowns to the Laplace equation from classic potential flow theory for the time evolution of a fluid air interface. At each time step, I need to solve a material derivative equation numerically at every node along an interface...