Ghost cells are used in many CFD codes for boundary-condition handling.

However, for axisymmetric problems, in certan situation, the y of the center of a ghost cell may equal to 0 (see the example), which leads to singularity. How to avoid this?

Thanks a lot.

example: -----------------------

bounday cell: y=dy

boundary line: y=dy/2

ghost cell: y=0

If you use the staggered mesh scheme, the axial and angular velocities (for a rotational flow) are located at y = dy/2, just above the y = 0 axis. The radial velocity is located on the edge of the cell, y = y_0, y_1, etc.

If your problem goes to the axis (y_0 = 0), the radial velocity must be 0 at the axis and is set AT the boundary - the boundary condition replaces the difference equation and is coded directly in you boundary condition routine. The axial velocity w is determined by dw/dz = 0 (symmetry) on the axis. Even with y = 0, your ghost cell setting of w(ghost) = w(first real cell) will set the shear correctly. Same thing applies to the angular (rotational) velocity.

Thanks.