The coupling of anisotropic unstructured mesh adaptation techniques with immersed boundary method (IBM) is studied for time dependent flow simulations involving moving objects. This work is incorporated within the framework of the European STORM project, with the aim (among others) to improve accuracy of simulation tools for ice shedding trajectories. The moving objects considered here are ice blocks detached from the aircraft after the use of a de-icing system. Their trajectories are required to predict if sensitive parts of the propulsive system could be damaged. The starting point of our work is an IBM method known as penalization introduced by Brinkmann in 1947 for a swarm of particles. In this approach a source term is added to the NS equations to account for the momentum defect related to the movement of the body, and representative of the forces exchanged between the fluid and the solid. We propose a complete study for solving unsteady penalized equations based on a Strang splitting approach. It allows to solve separately the NS part of the equations and the penalization part with a global second order accuracy in space and time. This approach has three main advantages. First, because of time step restriction, penalization has to be solved implicitly and therefore, the splitting allows flexibility in the choice of the scheme for the NS part (explicit scheme for instance, under condition of second order accuracy). Secondly, force computations can be performed using the change of momentum technique presented in. Finally, this splitting leads to a point by point resolution of the penalized part implying no matrix inversion, this matrix being potentially ill conditioned owing to the penalty parameter. To reduce the error on solid boundaries typically associated to IBM methods, we use unstructured mesh adaptation techniques. We present results of solids moved by a flow which requires a moving mesh in order to keep this adaptation. Thus, ALE residual distribution schemes are employed for solving the NS part of the splitting, combined to an exact solution of the ordinary differential equationsrunning the penalized part (over an asymptotic approximation with respect to the penalty parameter).