CFD Online Discussion Forums - Hard time on Transonic Linearized potential equation

Hi

I've been working on a code for the discretization of the Transonic linearized equation on a flow past a biconvex airfoil.

Code:

 (                               M²_inf            )   

 (1-M²_inf  - (g +1) --------------phi_x     ) phi_xx + phi_yy  = 0

 (                                U_inf            )

Where M_inf is the undisturbed mach number, phi is the potential, g=Cv/Ct, d phi/ dx = u, d phi/ dx = v.

I'm using a 2nd order discretization for 2nd derivatives, central in Y, and backward in X, and linearizing the term between brackets, recalculating it, at each iteration, using the new phi field. The 1st derivative in x is upwind.

I'm having a hard time making the solution converge and it's about the 4th time I rebuild the code and debug the results step by step.

So my guess is, the boundary conditions aren't well posed. There's little information freely available on the internet, and although I've found the topic on several books, they don't go into great detail.

Has anyone solved this problem. Is there a trick that I'm missing?

Thanks

S.