axisymmetric problem
hello! I have got a question about axisymmetric boudary condition. I developed a euler code for axisymmetric analysis, so now i'm validating the code with a cone. Then, i put solid wall(slip condition) and farfied boundary condition on boundary. The problem is that convergence don't go to machine precision. Does it need another condition for axis of symmetry? please reply me.

Re: axisymmetric problem
Can you describe the topology of your grid? For example: Does the cone extend all the way to the farfield? Is the grid 2D or 3D? Are your equations in polar coordinates or Cartesian coordinates...?

Re: axisymmetric problem
hi! I used the 2Dgrid from NPARC verification grid. Visit this site http://www.grc.nasa.gov/WWW/wind/val...10/cone10.html It makes you easy to understand. The equations is from 2D Euler equations in radial(r) and aixal(z) direction.

Re: axisymmetric problem
Since you say 'axisymmetric' and you are using the cylindrical coordinate system, there should be a source term in the governing equations related to centrifugal (or centripetal) acceleration, so the equations are not the same as the Cartesian 2D equations. Did you include that source term?
Have you tried solving the Cartesian 2D problem (not axisymmetric, but real 2D)? Is your flow purely supersonic as in the NPARC case? If not, you'll run into problems with the boundary conditions. How is your freestream bc defined? 
Re: axisymmetric problem
Dear Mani! Thanks for reply. My 2D code include that source term, and i already checked Catesian 2D(not axisimeetric) code using symmetry airfoil in supersonic flow. In case of freestream bc, I set supersonic inflow bc. Then i checked my soluion,actually mach number contour, The solution is good but convergence is not. For axisymmetric case, Is it possible to set Solid wall bc on the rotational axis(or axis of symmetry)?

Re: axisymmetric problem
In the supersonic case the freestream, inflow, outflow boundary conditions are very simple. They shouldn't give you any convergence problems. Yes, you should be able to use a symmetry condition (identical to solid inviscid wall) on the rotational axis. There is the issue of singularity on the axis (radius=0), but with a cellcentered finite volume scheme you shouldn't have any problem dealing with that. So right now it's hard to give a longdistance diagnosis. I would do this: Check if your convergence is good for a 2D wedge (not axisymmetric cone), using the 2D Cartesian equations (just remove the source term). If that doesn't converge any better, then your problem is likely not related to axisymmetry.

Re: axisymmetric problem
Dear Mani. I'll try your suggetions. Thank you.

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