3D case of prandtl-meyer expansion
 

what you have said pleasantly hold for a neck like ___________ ___________ > where r is large.

but does it also hold for a neck where the neck radius is quite small.like in my case the -- --> _________ flow ---<_________ - ---> |

| i have

to apply the turning here.

at r->0

(1). In the book "elements of gasdynamics" by Liepmann and Roshko, published by John Wiley & Sons, exercise of Chapter 12, problem 12.3, it says "Show that in the expansion over the shoulder of an axially symmetric body the pressure change is given by the two-dimensional, Prandtl-Meyer theory. Hint:Just at the shoulder,(1/w)*(dw/ds) is much greater than (sin(theta))/r." (2). The equation of motion for axially symmetric flow is given by equation-12.10. See Chapter-12, the method of characteristics. (3). In other words, 2-D Prandtl-Meyer theory (or approximation) is good for axially symmetric flow over the shoulder.

Re: 3D case of prandtl-meyer expansion
 

(1). Small is relative. As long as it is not "zero", it should be all right. (2). After all, it is just one local area. (3). I am getting the feeling that if you still have the question, then it is better to buy a commercial CFD code and then ask additional questions in the commercial codes forum. (just a joke) Don't be afraid of trying out different approaches. You may also want to try the MOC , because it is the exact method for supersonic inviscid flow.