Set a set of circular initial conditions on a mesh

jinwon park

I am solving 2-D compressible flows. As an initial condition, a high-pressure circle is embedded on a cartesian mesh. Currently, I am using the way like sqrt((x-xc)^2+(y-yc)^2). However, it produced a stair-case irregular something which is not a real circle. It may cause instability at later time and lead to the sudden abortion of codes. I am finding the way to get a real circle as possible. Is there a good way to set circular initial condition on a cartesian mesh? I really need your help all. Thanks in advance.