  Smoothed Particle Hydrodynamics (SPH) is a ubiquitous numerical method for
solving the fluid equations, and is prized for its conservation properties,
natural adaptivity, and simplicity. We introduce the Sphenix SPH scheme, which
was designed with three key goals in mind: to work well with sub-grid physics
modules that inject energy, be highly computationally efficient (both in terms
of compute and memory), and to be Lagrangian. Sphenix uses a Density-Energy
equation of motion, along with variable artificial viscosity and conduction,
including limiters designed to work with common sub-grid models of galaxy
formation. In particular, we present and test a novel limiter that prevents
conduction across shocks, preventing spurious radiative losses in feedback
events. Sphenix is shown to solve many difficult test problems for traditional
SPH, including fluid mixing and vorticity conservation, and it is shown to
produce convergent behaviour in all tests where this is appropriate. Crucially,
we use the same parameters within Sphenix for the various switches throughout,
to demonstrate the performance of the scheme as it would be used in production
simulations.
