axisymmetry.. again..

queram

guys, I have a FVM solver (MacCormack method) for 2D planar flows (euler equations). Now I'm modifying it to 2D axisymmetric. I've fixed boundary conditions (solid wall (no-slip), inlet, outlet, centerline), developed appropriate mesher etc. The code works nicely, even the results look OK. But: the equations in the solver remained the same as for 2D planar case. Is it a big mistake? Most of the books I went through say nothing on this, just few (ferziger-peric among them) say "the same code can be used for 2D planar and 2D axisymmetric cases, just to set x=z and y=r". Looking at the equations: 2D planar: dW/dt+dF/dx+dG/dy=0, where W=(rho, rho*u, rho*v, rho*e) F=(rho*u, rho*u^2+p, rho*u*v, rho*u*h) G=(rho*v, rho*u*v, rho*v^2+p, rho*v*h)

and 2D axisym: dW/dt+dF/dz+dG/dr+1/r*R=0, where W=(rho, rho*u, rho*v, rho*e) F=(rho*u, rho*u^2+p, rho*u*v, rho*u*h) G=(rho*v, rho*u*v, rho*v^2+p, rho*v*h) R=(rho*v, rho*u*v, rho*v^2, rho*v*h)

z=x, r=y, u is in x(z) direction, v is in y(r) direction; theta=0.

obviously, 2D axisym case has the R term extra. If I don't use I'll......? If I use it, any idea how to dicretize it?