We present calculations and analyses of 3D vortices in accretion disks around protostars. We also compute the effect of the vortices on the transport of energy, momentum and dust particles. The numerical computations are challenging because the environment is highly-stratified, rotating, shearing and turbulent, and the resulting flows have breaking internal gravity waves, vortex collisions, and structures with thin internal layers. Because the main astrophysical interest in the calculations is the understanding of the transport and because the transport is sensitive to small-scale structures, high resolution is required. Consider angular momentum.The vortices transport angular momentum radially away from the protostar, enabling mass to accrete onto the protostar at the observed rates. However, accretion occurs only when local symmetries are broken during vortex-vortex encounters, so the results require high space and time resolution during the collisions. The vortices are created baroclinically from the small thermal fluctuations that are themselves created by the breaking of the gravity gravity waves, so it is necessary to compute the breaking with great accuracy. The vortices accumulate dust grains, which, depending how agglomeration is modeled, can produce the planetesimals from which planets are made. However, the basins of attraction of the grains depend on the details of the turbulent vortices; at some places and at some times the attractor is a point, while at others it is a limit cycle (orbit). The volume of the basins determine whether planetesimals form, so accuracy is needed in these calculations as well. The calculations are pseudo-spectral using mapped basis functions. We review some of the numerical techniques we developed to allow us to carry out the calculations when the gas density in the domain of interest
varies by a factor of 10,000 and when there are similar ranges in the length and time scales of interest.
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