If the body is moving, then the grid attached on it is moving, too. But I don't use refference on the body.

For time t, assuming I get the flow field at t+dt and velocity of the body. Then I move the body and grid. But how can I get those flow state on the new grid?

There are two ways:

1. Decoupled. solve flowfield of t+dt using grid at t.

Then move the body explicitly.

2. Iterative. The above two procedures are repeated

untill a certain convergence is obtained. I think you need do the second way.