What can anybody tell me about 3D characteristic methods? Are they practical? Are they any faster than solving the Euler equations? Surely there is a savings in grid generation. I'm wondering if there's any possibility to use such an approach to guide or optimize the design of supersonic vehical surfaces.

2-D and 3-D method of characteristics have been used in external flow, internal flow and aerodynamic testing for many years. Mehtod of characteristic is an exact method. It can be implemented using graphic method or numerical method. The limitation is: it is not for subsonic flow. The method of characteristics has been used to guide the design of more accurate and advanced schemes for solving the Euler equations. ( Numerical methods for Euler equations are approximate in nature, and the shock is captured in an approximate sense. Numerical solutions of Euler equations are not truely inviscid, because of the viscous effect created by the numerical diffusion or added artificial diffusion terms.) Thinking about re-inventing the wheel? It may not be a bad idea after all. Things are being re-invented all the time. ( I think 'CFD mechanics' was invented by the old generation for the people in the computer age.)

A good reference for MOC I would recommend is Gas Dynamics (Vol II) by M.J. Zucrow and J.D. Hoffman.