[hadesmajesty]

I am simulating a small amplitude TS wave in the boundary layer by finite difference method. At the freestream boundary I impose a Robin boundary condition, that is, du/dy=-a*u, indicating that the wave velocity decays exponentially at the freestream boundary.
However, my numerical solution is not correct at the region near the freestream boundary (the other part seems correct). I try to make an exponential regression and find that the decay rate is about 2*a rather than a, as in my boundary condition.
I have tried to use different schemes to discretize this condition, but the phenomenon still comes up.
Is it because of some bugs in my code or the incorrect discretisation of the Robin boundary conditions? An suggestions to solve this problem?
Thank you in advance.