A tensor artificial viscosity for SPH

A tensor generalization of the Monaghan-Gingold artificial viscosity for smoothed particle hydrodynamics (SPH) is formulated. We also develop a new limiter to restrict the effects of the artificial viscosity to the direction of shock travel, while maintaining enough of the artificial viscous dissipation to keep the SPH technique stable. We present a series of test problems comparing the new viscosity formalism with the standard method for fluid flows in two and three dimensions, such as shearing systems undergoing shocks. We also present tests of the conservation and transport of angular momentum, since total angular momentum conservation is not guaranteed with the new viscosity formalism.