Boundary condition in Finite different scheme

It's time to keep track of my progress in PhD program.

While solving the 1-D in duct problem with finite different (FD) scheme (please go to the project page for more accurate detail: http://acoubulence.zxq.net/), implementing the boundary condition, as well as the numerical integral, is a tricky part to such a beginner like me.

The homogeneous Dirichlet condition is sort of easier to make; but the homogeneous Dirichlet condition at the center of the duct is not that straightforward. Since the FD scheme I am using now is central FD, an extrapolated point is set to describe the derivative of the center point, but the calculated results were incorrect.

After talking with Ardeshir I am going to use forward difference at the center point instead. Actually I am still curious about what the results will look like if using two FD scheme in one simulation. I will try to show the results (hope are positive ones) in the next post.