FARGO: A fast eulerian transport algorithm for differentially rotating disks

We present an efficient and simple modification of the standard transport a lgorithm 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 fas t orbital motion at tl-le inner boundary. In tl-lis modified algorithm, the timestep is limited by the perturbed velocity and by the shear arising fro m the differential rotation. FARGO stands for "Fast Advection in Rotating G aseous Objects". The speed-up resulting from the use of the FARGO algorithm is problem dependent. In the example presented here, which shows the evolu tion of a Jupiter sized protoplanet embedded in a minimum mass protoplaneta ry nebula, the FARGO algorithm is about an order of magnitude faster than a traditional transport scheme, with a much smaller numerical diffusivity.