what are the non-reflecting condition (compressible flow) for the farfield boundaries in terms of density, pressure and velocity components?

Shuo

I read a paper by K.W.Thompson Jour.Comp.Phys 68, 1987 which gave the non-reflecting characteristic equation in cartesian coordinates. I am working in cylindrical coordinates. Not sure how to convert it. Shuo

There is a recent paper "Generalized Characteristic Boundary Conditions for Computational Aeroacoustics, Part 2" by Kim and Lee and also check the part 1 of it.Both the papers which are tension of the paper of Poinsot and Lele(1992,JCP) discuss the implementation of characteristic BC in generalized coordinates. I do not have their electronic version.

What about the symmetry condition in x-r coordinates? Is that given as well?

The papers do not discuss the symmetry boundary condition but the implementation would be very similar to other BC where you define incoming characteristic in terms of outgoing characteristics.Hirsch has a discussion I think on the implementation of characteristics for symmetry.