Planets form in protoplanetary disks which are rotating structures of gas and dust surrounding young stars. Before a protoplanetary disk disperses, the mass of gas dominates over the mass of solids and thus the evolution of the disk and planets is driven by hydrodynamic phenomena. Although this evolutionary stage does not last longer than several million years, it inevitably predetermines the properties of the emerging planetary system, i.e. the multiplicity of planets, their orbital configuration, distances from the central star, their masses and types (whether they become terrestrial or gas giants). Understanding the impact of hydrodynamic processes on planet formation can help us understand the great diversity among the observed extrasolar planetary systems.
First, I will demonstrate the variety of hydrodynamic processes in protoplanetary disks by reviewing several examples, e.g. instabilities leading to angular momentum transport, instabilities enhancing accretion of solids, and planet-disk interactions leading to planetary migration. Next, I will describe numerical solution of the fluid equations within the framework of so-called FARGO hydrodynamic codes (Masset 2000, Benítez-Llambay & Masset 2016) which are often used to study planet-disk interactions. I will present a recent 2D model focused on interactions of multiple planets with a gas disk and a coupled disk of pebbles (Chrenko et al. 2017). Finally, I will outline a more advanced 3D model which is currently under development and I will discuss the implementation of radiative diffusion and stellar irradiation.