Modified FARGO algorithm and its combination with adaptive mesh refinement

Fast advection in rotating gaseous objects (FARGO, Masset (2000)) algorithm has been widely used in simulating disk-type object in computational astrophysics. In this paper, we revisit this algorithm and propose some improvement. We also propose a semi-Lagrangian adaptive mesh refinement for this algorithm to enhance resolution locally near the embedded proto-planet. Numerical tests are provided to demonstrate the effectiveness of our method.