moving cylinder

blur boy

Hi! I'm doing this code on an external body flow. Basically I need to use the standard 2D Cartesian coordinates (x,y) to compute the flowfield around a moving circular cylinder WITHOUT moving the cartesian grid. The frame is fixed and the cylinder is moving in a fixed prescribed velocity and I'm using the streamfunction-vorticity formulation of the Navier Stokes equation to compute.

Usually if the cylinder is fixed (not moving), we can derive the streamfunction at the cylinder by using the summation of (del operator x vorticity) along the cylinder surface. But for moving cylinder, that is not the case. Does anyone know what equation should I use to derive the cylinder streamfunction for the moving case?

Thank you!