Title:　 　 Numerical Study of Linear and Nonlinear Density Wave Evolution in Protoplanetary Disks
　  Speaker:　  Professor Dong ruobing (Princeton University) 
　　Time:　　   2pm, Tuesday (June 21)
　  Location:　 big conference room, 3rd floor

Abstract:
With very high spatial resolution, accurate numerical algorithm, and precise planetary potential, we carry out 2D shearing sheet simulations to provide detailed quantitative comparisons of numerical results with both linear and nonlinear analytical theories on the density waves excited by low mass planets in protoplanetary disks. We achieve very good agreement (at the level of several percent) with theories on primary physical variables,including the spatial distributions of the surface density perturbation,planetary torque (in both physical and Fourier space), the growth and damping of the angular momentum flux carried by the wave. The behavior of the potential vorticity generation at the nonlinear shock is studied analytically, which we use to pinpoint the shock and verify the theoretical shocking length function. We explore several issues which are ignored by the analytical theories. The effects of various numerical parameters are extensively investigated, based on which we provide a framework for future code test in the field of planet-disk interactions. Finally, we discover a commonly ignored but important numerical issue related to the FARGO algorithm, which if not handled correctly will lead to incorrect numerical results and an artificial gap opening phenomenon.