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Multi-Frequency General Relativistic Radiation-Hydrodynamics with $\bf{M}_1$ Closure

We report on recent upgrades to our general relativistic radiation-magnetohydrodynamics code, Cosmos++, which expands the two-moment, $\bf{M}_1$, radiation treatment from grey to multi-frequency transport, including Doppler and gravitational frequency shifts. The solver accommodates either photon (Bose-Einstein) or neutrino (Fermi-Dirac) statistical distribution functions with absorption, emission, and elastic scattering processes. An implicit scheme is implemented to simultaneously solve the primitive inversion problem together with the radiation-matter coupling source terms, providing stability over a broad range of opacities and optical depths where the interactions terms can be stiff. We discuss our formulations and numerical methods, and validate our methods against a wide variety of test problems spanning optically thin to thick regimes in flat, weakly curved, and strongly curved spacetimes.