FARGO: A fast eulerian transport algorithm for differentially rotating disks

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 than 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.