SPHS: Smoothed Particle Hydrodynamics with a higher order dissipation
  switch
  We present a novel implementation of Smoothed Particle Hydrodynamics (SPHS)
that uses the spatial derivative of the velocity divergence as a higher order
dissipation switch. Our switch -- which is second order accurate -- detects
flow convergence before it occurs. If particle trajectories are going to cross,
we switch on the usual SPH artificial viscosity, as well as conservative
dissipation in all advected fluid quantities (for example, the entropy). The
viscosity and dissipation terms (that are numerical errors) are designed to
ensure that all fluid quantities remain single-valued as particles approach one
another, to respect conservation laws, and to vanish on a given physical scale
as the resolution is increased. SPHS alleviates a number of known problems with
`classic' SPH, successfully resolving mixing, and recovering numerical
convergence with increasing resolution. An additional key advantage is that --
treating the particle mass similarly to the entropy -- we are able to use
multimass particles, giving significantly improved control over the refinement
strategy. We present a wide range of code tests including the Sod shock tube,
Sedov-Taylor blast wave, Kelvin-Helmholtz Instability, the `blob test', and
some convergence tests. Our method performs well on all tests, giving good
agreement with analytic expectations.
