We present the results of a three dimensional, locally isothermal, non-self-gravitating SPH code which models protoplanetary disks with two fluids: gas and dust. We ran simulations of a 1 M star surrounded by a 0.01 M disk comprising 99% gas and 1% dust in mass and extending from 0.5 to ∼300 AU. The grain size ranges from 10 −6 m to 10 m for the low resolution (∼25 000 SPH particles) simulations and from 10 −4 m to 10 cm for the high resolution (∼160 000 SPH particles) simulations. Dust grains are slowed down by the sub-Keplerian gas and lose angular momentum, forcing them to migrate towards the central star and settle to the midplane. The gas drag efficiency varies according to the grain size, with the larger bodies being weakly influenced and following marginally perturbed Keplerian orbits, while smaller grains are strongly coupled to the gas. For intermediate sized grains, the drag force decouples the dust and gas, allowing the dust to preferentially migrate radially and efficiently settle to the midplane. The resulting dust distributions for each grain size will indicate, when grain growth is added, the regions when planets are likely to form.

We describe a parallel, cosmological N-body code based on a hybrid scheme using the particle-mesh (PM) and Barnes-Hut (BH) oct-tree algorithm. We call the algorithm GOTPM for Grid-of-Oct-Trees-Particle-Mesh. The code is parallelized using the Message Passing Interface (MPI) library and is optimized to run on Beowulf clusters as well as symmetric multi-processors. The gravitational potential is determined on a mesh using a standard PM method with particle forces determined through interpolation. The softened PM force is corrected for short range interactions using a grid of localized BH trees throughout the entire simulation volume in a completely analogous way to P 3 M methods. This method makes no assumptions about the local density for short range force corrections and so is consistent with the results of the P 3 M method in the limit that the treecode opening angle parameter, θ → 0.The PM method is parallelized using one-dimensional slice domain decomposition. Particles are distributed in slices of equal width to allow mass assignment onto mesh points. The Fourier transforms in the PM method are done in parallel using the MPI implementation of the FFTW package. Parallelization for the tree force corrections is achieved again using one-dimensional slices but the width of each slice is allowed to vary according to the amount of computational work required by the particles within each slice to achieve load balance. The tree force corrections dominate the computational load and so imbalances in the PM density assignment step do not impact the overall load balance and performance significantly. The code performance scales well to 128 processors and is significantly better than competing methods. We present preliminary results from simulations run on different platforms containing up to N = 1G particles to verify the code.

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