Help for cut cell scheme for moving problems

Wei

Anyone here 've experience in cartesian grid cut cell method?

I've just coded one which is similar to that of Mittal/Ye et. al. It has worked for stationary body.

however, i've met with problems when i run it for oscillating cylinder. My cl/cd is very irregular instead of periodic.

I'm using FVM CN2 scheme to discretise and hence in the momentum eqn, I need to to compute values at old time step=n.

1. For the old values, do I compute them at the new position or old position?

2. If I need to compute them at the new position, how do I calculate the boundary value? They are prescribed but at t=n+1 and n, they are at different location. So how should I calculate it at the new location but at t=n?

Thanks a lot.