Planet formation: The case for large efforts on the computational side

Modern astronomy has finally been able to observe protoplanetary disksin reasonable resolution and detail, unveiling the processes happening during planet formation. These observed processes are understood under the framework of disk-planet interaction, a process studiedanalytically and modeled numerically for over 40 years. Long a theoreticians' game, the wealth of observational data has been allowing for increasingly stringent tests of the theoretical models. Modeling efforts are crucial to support the interpretation of direct imaging analyses, not just for potential detections but also to put meaningful upper limits on mass accretion rates and other physical quantities in current and future large-scale surveys. This white paperaddresses the questions of what efforts on the computational side are required in the next decade to advance our theoretical understanding, explain the observational data, and guide new observations. We identified the nature of accretion, ab initio planet formation, early evolution, and circumplanetary disks as major fields of interest in computational planet formation. We recommend that modelers relax the approximations of alpha-viscosity and isothermal equations of state, on the grounds that these models use flawed assumptions, even if they give good visual qualitative agreement with observations. We similarly recommend that population synthesis move away from 1D hydrodynamics. The computational resources to reach these goals should be developed during the next decade, through improvements in algorithms and the hardware for hybrid CPU/ GPU clusters. Coupled with high angular resolution and great line sensitivity in ground based interferometers, ELTs and JWST, these advances in computational efforts should allow for large strides in the field in the next decade.