i am trying to find the flow field around a two stepped cone (axisymmetric case) using McCormak's predictor corrector scheme for shock capturing .Since it is axisymmetric,the problem has become more of a 2d problem and i am solving the eqn:

dE/dx+dF/dy+H=0 where E,F and H are the conventional flux vectors for the strong conservative form.but the problem is that in H i am having a "1/y" factor that becomes undefined at y=0. i have used some limits and have changed the governing equations (continuity,x-mom,y-mom etc ) for y=0 case. here there is another problem. while just at the beginning of the cone,where y=0, i am using this modified eqn in the predictor step . but on the corrector step, since i have already moved a bit up on the cone and y is no longer=0,i am using the above form (ie without applying any limits like y-->0)for the corrector step.will this cause serious errors in the code? also where can i get some material relating to this work.? while pressure on the surface of the first cone should remain constant since it forms a ray, in my case it is steadily decreasing. why is it so ?

From my limited knowledge:

(1) Do a geometric conservation check. Find the solution in a domain containing no solid body. Assign Free stream flow.

(2) At the centerline, only for boundary conditions use L'hopital rule. If your scheme is cell vertex. If cell center you should have no problem representing the boundary conditions.

(3) Check your source term handling method once again.

Hope this helps.

k.

(1). For axisymmetric 2-D problem, there is a simple method to deal with the centerline singularity. (2). All you need to do is to attach a very thin cylinder to the tip of the cone. You can treat the boundary condition there as symmetric condition. (3). I had used the method many years ago for flow over a cone, and there was no problem as far as I can remember. (4). The method was to solve the Navier-Stokes equations, and it requires artificial viscosity term in the form of higher order pressure derivatives. The method was very popular in 70' and 80's. Look at the publications from NASA/Ames, Air Force research labs and AIAA journals in that period of time.

thank you for your help.i have two more queries.

1)can i use the form of Abett's method we use for boundary correction in the 2D case for correcting boundary condition in the 3d case as well (ie for my axisymmetric case as well)?

2)in the axisymmetric case, is it justified to do boundary corrections both after the predictor and corrector steps instead of applying the boundary condition only once after the predictor-corrector pair.