Modelling the Disk (three-phase) Interstellar Medium

The evolution of galactic disks from their early stages is dominated by gas dynamical effects like gas infall, galactic fountains, and galactic outflows, and more. The influence of these processes is only understandable in the framework of diverse gas phases differing in their thermal energies, dynamics, and element abundances. To trace the temporal and chemical evolution of galactic disks, it is therefore essential to model the interstellar gasdynamics combined with stellar dynamics, the interactions between gas phases, and star-gas mass and energy exchanges as detailed as possible. This article reviews the potential of state-of-the-art numerical schemes like Smooth-Particle and grid-based hydrodynamics and their ingredients, such as star-formation criteria and feedback, energy deposit and metal enrichment by stars, and the influence of gas-phase interactions on the galactic gas dynamics and chemistry.