Formation of cold molecular filaments in cooling flow clusters

New CO observations at the center of cooling flow in Perseus cluster \cite{salome06} show a clear correlation of the molecular gas with the previously detected H-$\alpha$ filaments \cite{conselice01}. In this poster, we present high resolution multi-phase simulations of the Perseus Cluster, taking into account the AGN feedback in form of hot buoyant bubbles. These simulations show that significant amount of gas can cool far from the center. The AGN feedback provides some heating, but also trigger the hot gas compression, that favours cooling (positive feedback), even at high radius ($R>30 \rm{kpc}$). The cooled gas flows into the cluster core forming the observed filaments.