FARGO: a fast eulerian transport algorithm for differentially rotating disks

Abstract

We present an efficient and simple modification of the standard transport algorithm used in explicit eulerian fixed polar grid codes, aimed at getting rid of the average azimuthal velocity when applying the Courant condition. This results in a much larger timestep then the usual procedure, and it is particularly well-suited to the description of a Keplerian disk where one is traditionally limited by the very demanding Courant condition on the fast orbital motion at the inner boundary. In this modified algorithm, the timestep is limited by the perturbed velocity and by the shear arising from the differential rotation. FARGO stands for ``Fast Advection in Rotating Gaseous Objects''. The speed-up resulting from the use of the FARGO algorithm is problem dependent. In the example presented here, which shows the evolution of a Jupiter sized protoplanet embedded in a minimum mass protoplanetary nebula, the FARGO algorithm is about an order of magnitude faster than a traditional transport scheme, with a much smaller numerical diffusivity.

9 pages, 6 figures. Accepted for publication in Astron. Astrophys. Supp. Series

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• Adapting a solid accretion scenario for migrating planets in FARGO3D
• Effects of turbulent diffusion and back-reaction on the dust distribution around two resonant planets
• Disentangling Planets from Photoelectric Instability in Gas-Rich Optically Thin Dusty Disks
• How two-dimensional are planet-disc interactions? II. Radiation hydrodynamics and suitable cooling prescriptions
• Pade: A code for protoplanetary disk turbulence based on Pade differencing
• Planet-driven density waves in protoplanetary discs: numerical verification of nonlinear evolution theory
• Hydrodynamical models of the $\beta$ Lyr A circumstellar disc
• Hydrodynamical simulations with strong indirect terms in Fargo-like codes: Numerical aspects of non-inertial frame and artificial viscosity
• Long-term Hydrodynamic Simulations on the Planetesimals Trapped in the First-order Mean Motion Resonances
• Low mass planet migration in Hall-affected disks
• Mass flow in the circumbinary disk with gap around supermassive binary black holes
• Gas and dust dynamics in $\gamma$ Cephei-type disks
• Selfgravitating disks in binary systems: an SPH approach -- I. Implementation of the code and reliability tests
• Modelling the evolution of planets in disks
• Dust-driven vortex cascades originating at water snow regions: A pathway to planetesimal formation