| Summary: | The formation and evolution of protoplanetary disks is simulated by computer modelling, using the Smoothed Particle Hydrodynamics (SPH) method. The suitability of SPH for modelling disks is investigated, and problems are identified with the SPH implementation of Artificial Viscosity in disks with Keplerian velocity profiles. Analytical and experimental results reveal that the resultant viscous force for a simulated Keplerian disk is in the opposite direction to that produced by linear shear. Applying Artificial Viscosity only to approaching particles results in a radial force four times larger than the force in the direction of the orbit. The viscous force can change direction if temperature, and therefore sound speed, decreases. Techniques for activating Artificial Viscosity only when convergence is detected are found to fail in differentially rotating disks. Both the Balsara Switch and Time Dependent Artificial Viscosity use the SPH estimate of V v sph, which has a low freqency time varying component which is independent of h, and so cannot be removed by increasing the number of SPH particles. An alternative method, based on pattern recognition, is shown to reduce the viscous spread of a differentially rotating ring by an order of magnitude. We also identify problems associated with the gravitational field of disks. The use of an annulus to represent a portion of a much larger, continuous disk, may yield unrepresentative results. The edge effects can cause preferential accretion zones, where the Toomre Q parameter is not the same as it would be for the same region of an extended disk. SPH simulations of Protoplanetary disks produce condensations which do not persist long enough to collapse. The high tidal shearing forces in a Keplerian accretion disk disrupt the condensations before they accumulate enough mass to collapse. Including a more realistic treatment of the thermal physics, and reducing the effective shear viscosity, makes the situation worse.
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