Discontinuous-Galerkin Representation of the Maxwell-Juttner Distribution

Accurately projecting the Maxwell-Juttner (MJ) distribution onto a discrete simulation grid can be a challenge for relativistic kinetic continuum simulations. This arises from the finite velocity bounds of the domain which may not capture the entire distribution function, as well as errors introduced by projecting the function onto a discrete grid. Here we outline a procedure for projecting the MJ in a Discontinuous Galerkin scheme, which itself adds complication in calculating nonlinear quantities on the grid. By computing the moments of the projected distribution function, using Gauss-Legendre quadrature for nonlinear quantities, and iterative correcting moments calculated by this procedure they converge, we can correct for these inaccuracies in the discrete projection. The result is a method that accurately captures the distribution function and ensures the moments match the desired values to machine precision.