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Multi-messenger astrophysics has produced a wealth of data with much more tocome in the future. This enormous data set will reveal new insights into thephysics of core collapse supernovae, neutron star mergers, and many otherobjects where it is actually possible, if not probable, that new physics is inoperation. To tease out different possibilities, we will need to analyzesignals from photons, neutrinos, gravitational waves, and chemical elements.This task is made all the more difficult when it is necessary to evolve theneutrino component of the radiation field and associated quantum-mechanicalproperty of flavor in order to model the astrophysical system of interest -- anumerical challenge that has not been addressed to this day. In this work, wetake a step in this direction by adopting the technique of angular-integratedmoments with a truncated tower of dynamical equations and a closure, convolvingthe flavor-transformation with spatial transport to evolve the neutrinoradiation quantum field. We show that moments capture the dynamical features offast flavor instabilities in a variety of systems, although our technique is byno means a universal blueprint for solving fast flavor transformation. Toevaluate the effectiveness of our moment results, we compare to a more preciseparticle-in-cell method. Based on our results, we propose areas for improvementand application to complementary techniques in the future.

Two-Moment Neutrino Flavor Transformation with applications to the Fast Flavor Instability in Neutron Star Mergers