Plz. Need your help: Circular I.C on 2D problem
 

Please help me how to setup the initial condition.

I have a circle of radius 0.2 centered (1,1) in domain 2*2.

There are two initial condition sets separated by the circle.

Since the mesh is a cartesian, the staircase configurations were shown across the circle. Some authors mentioned that the initial conditions should be modified on quadrilaterial cells cutting the initial disconitnuity(i.e circle) by assigning modified-area-weighted value to appropriate cells at t=0.0sec.

In fact, that's basic but I haven't had such experience before. Please teach me how to setup the circular initial condition on the quadrilaterial cells at time t=0.0