  The motivating question for this dissertation was to identify the minimal
requirements for fluid models of plasma to allow converged simulations that
agree well with converged kinetic simulations of fast magnetic reconnection. We
show that truncation closure for the deviatoric pressure or for the heat flux
results in singularities. Due to the strong pressure anisotropies that arise,
we study magnetic reconnection with a Gaussian-moment two-fluid MHD with
isotropization of the pressure tensor. For the GEM magnetic reconnection
challenge problem, our deviatoric pressure tensor agrees well with published
kinetic simulations at the time of peak reconnection, but sometime thereafter
the numerical solution becomes unpredictable and develops near-singularities
that crash the simulation unless positivity limiters are applied. To explain
these difficulties, we show that steady reconnection requires heat flux.
Specifically, for two-dimensional problems invariant under 180-degree rotation
about the X-point, entropy production in the vicinity of the X-point is
necessary for reconnection and causes solutions to become singular for
conservative models that lack heat flux. This prompts the need for a 10-moment
gyrotropic heat flux closure. Using a Chapman-Enskog expansion with a
Gaussian-BGK collision operator yields a heat flux closure for a magnetized
10-moment charged gas which generalizes the closure of McDonald and Groth.
