Realizability-Preserving DG-IMEX Method for a Two-Moment Model of Special Relativistic Transport

Speaker: Joseph Hunter (OSU)
Dates: 2023/11/01
Location: MA 105
Abstract: Special relativistic transport models are important for describing the transport of neutrinos, with applications to supernovae and gravitational waves.  We study a two-moment model that evolves the Eulerian moments of a particle distribution function $f$.  Due to physical bounds on the distribution function, $f \geq 0$, we want a numerical method which preserves these bounds on the evolved moments.  Such moments are said to be realizable.  The model is not closed in terms of the evolved moments, and thus requires a closure procedure.  As a result of this, it is necessary to recover Lagrangian moments of $f$ from the evolved Eulerian moments.  The proposed realizability-preserving scheme uses the discontinuous Galerkin (DG) method to discretize space and uses an implicit-explicit (IMEX) time integration method.  Moment realizability is preserved through the appropriate choice of numerical spatial and numerical energy fluxes. This yields a realizability-preserving timestep restriction for the IMEX method.  In addition, we require the moment recovery process to be realizability-preserving, since the recovery process can be extended to the nonlinear solve required in the IMEX method.