Dissipative Magnetohydrodynamics for Non-Resistive Relativistic Plasmas: A flux-conservative formulation with stiff relaxation

  Based on a 14-moment closure for non-resistive viscous plasmas, we 

  describe a new numerical scheme that includes all (first-order) dissipative effects (heat

  conduction, bulk- and shear viscosity). By solving an extended system

  for the dissipative quantities that enforces algebraic constraints via

  stiff-relaxation, we are able to cast all first order dissipative terms

  in flux-divergence form. This allows us to apply traditional

  high-resolution shock capturing methods to the equations, making the

  system suitable for the numerical study of highly turbulent flows.

  The 14-moment closure can seamlessly interpolate between the highly

  collisional limit found in neutron star mergers and heavy-ion collisions, and the weakly coupled

  Braginskii-like limit of extended MHD appropriate for the study of

  accretion disks. Hence, we believe that this new formulation and

  numerical scheme will be useful for a broad context of relativistic

  (magnetized) flows in heavy-ion collisions and astrophysics.