We have developed a simulation tool (LA-COMPASS) for dusty proto-planery disks. The proto-planetary disk is treated as a three-dimensional(3D), self-gravitating gas, whose motion is described by the Navier-Stokes equations, coupled to a similar (pressureless) system of equations for the dust in a spherical coordinate centered on the star. The two sets of equations for gas and dust particles are coupled via drag terms. A second-order high-resolution Godunov scheme is used to solve the equations numerically. A semi-Lagrangian method is implemented to remove the background Keplerian motion to alleviate the time step restriction in azimuthal direction. We also develop a fast solver for the disk self-gravity and coordinate acceleration due to the disk gravity.

　　We also develop a solver for proto-planetary motions. The coupling between the disk and planet motion is carefully considered. To improve the resolution near the planets, we develop a semi-Lagrangian adaptive mesh refinement (AMR) technique. Unlike traditional dynamic AMR, the refinement region in our AMR can move across a number of cells within one time step. The code is fully parallelized via message-passing interface coupled with OpenMP for multi-threads. We have verified the algorithm and code using several examples with exact solutions. We have used the code to simulate the dust distribution with and without planets, and obtained results that are in good agreement with observation data from ALMA