We present a versatile finite volume method for the simulation of incompressible flows past moving bodies. The Navier-Stokes equations are discretized on AMR enabled quadtree grids, where the dynamic in time refinement is adapted to the evolution of the fluid-solid system. The immersed bodies are modeled through a second-order penalization method and the interface is tracked using a level-set description. We highlight on two dimensional test cases that the uniform grids accuracy can be recovered using quadtree grids with less degrees of freedom.