some puzzles on Boundary condition transformation
 

Hello,everyone. I want to simulate a supersonic (Ma=4.0) flow fleid around a circular body and check for the shock/boundary profiles. I choose to use the finite difference method(FDM),and hence I do a grid transformation from physical domain(x,y) to computational domain(ξ,η). And there comes some puzzles:
Attachment 12550
1) on the physical outflow boundary the condition like ux(imax,j)=ux(imax-1,j) such interpolations, how to convert this to the computational domain ?

2) what scheme is suitable for super/hypersonic problems like this, MacCormack seems have strong oscilations around the shock. what about Ausm series?

3) During the grid transformation, is second-order estimation of Jacobians like Xξ sufficient?

Thank you very much for advises, my friends. I am looking forward for your help. :)

In your case you need one of shock-capturing schemes http://en.wikipedia.org/wiki/Shock_capturing_methods

Thank you for your reply and useful website.
for the puzzle 1 listed , can you give me some advices. I guess my code work fails largely on this boundary condition transformation.
Explicitly to say, like a adiabatic left wall boundary in physical plane(x,y),we may use T(1,j)=T(2,j) to specify, after the transformation on the computational plane (ξ,η), what the left wall boundary then should look like , it's a mathe problem in fact.
Thank you in advance. :)