# Two Dimensional Nozzle Flow

I've been looking at the book "Computational Fluid Dynamics - The Basics With Applications", by John D. Anderson, and his solution for the one-dimensional subsonic-supersonic nozzle flow using the MacCormack scheme. I was wondering if there are any book chapters or academic papers out there explaining, in the level of detail given by Anderson, how to solve two dimensional nozzle flow. I found the following AIAA paper, but cannot access it since I'm unfortunately not a member: http://arc.aiaa.org/doi/abs/10.2514/3.61365

Any help would be greatly appreciated.

• Are you asking for an analytical solution, or numerical? A classic method for solving 2D inviscid supersonic expanding nozzle is the method of characteristics, detailed in Anderson's "modern compressible flow" text. And the MacCormack scheme is certainly extendable to 2D and 3D. – Aurelius Nov 5 '14 at 15:20
• I'm looking for numerical solutions. I realise that his algorithms can be extended to 2D, but since I don't have too much experience in the subject matter I'm finding it very tough. In particular, how would I apply boundary conditions to the walls or the nozzle and what would the coordinate transformation look like? – indigoblue Nov 5 '14 at 15:39
• The next chapter in that Anderson CFD book (numerical simulation of the prandtl-meyer expansion fan) is a good place to start. An expanding nozzle is just like the corner in that geometry, except it's continually expanding. – Aurelius Nov 5 '14 at 15:51
• I'm currently working on the prantl-meyer section but am getting through it a lot slower than the previous sections since the explanations aren't as in-depth as before. – indigoblue Nov 5 '14 at 16:00
• Numerics for the radial nozzle (still 1D though) can be quite simple. Any interest in a write up there? – Rhys Ulerich Nov 6 '14 at 2:17