[YeChen]

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:
Fig.jpg
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.