  The main problems of nonvacuum numerical relativity, compact binary mergers
and stellar collapse, involve hydromagnetic instabilities and turbulent flows,
so that kinetic energy at small scales have mean effects at large scale that
drive the secular evolution. Notable among these effects is momentum transport.
We investigate two models of this transport effect, a relativistic
Navier-Stokes system and a turbulent mean stress model, that are similar to all
of the prescriptions that have been attempted to date for treating subgrid
effects on binary neutron star mergers and their aftermath. Our investigation
involves both stability analysis and numerical experimentation on star and disk
systems. We also begin the investigation of the effects of particle and heat
transport on post-merger simulations. We find that correct handling of
turbulent heating can be important for avoiding unphysical instabilities. Given
such appropriate handling, the evolution of a differentially rotating star and
the accretion rate of a disk are reassuringly insensitive to the choice of
prescription. However, disk outflows can be sensitive to the choice of method,
even for the same effective viscous strength. We also consider the effects of
eddy diffusion in the evolution of an accretion disk and show that it can
interestingly affect the composition of outflows.
