A fast eulerian transport algorithm for differentially rotating disks

Abstract. We present an ecient and simple modica-tion of the standard transport algorithm used in explicit eulerian xed 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 modi-ed algorithm, the timestep is limited by the perturbed velocity and by the shear arising from the dierential ro-tation. 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 exam-ple presented here, which shows the evolution of a Jupiter sized protoplanet embedded in a minimum mass proto-planetary nebula, the FARGO algorithm is about an order of magnitude faster than a traditional transport scheme, with a much smaller numerical diusivity