Griffin is a reactor physics application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE). This work discloses the methods, algorithms, and implementation for simulating heterogeneous reactor dynamics models. Griffin utilizes a discontinuous finite-element method with discrete ordinates (DFEM-SN) to discretize the multigroup neutron transport equation. Multiphysics feedback is handled using a two-step tabulated cross-section methodology. Feedback quantities are evaluated using the flexible MOOSE-MultiApp system to couple various physics, such as heat conduction, thermal fluids, and fuel performance. The multiphysics DFEM-SN system is solved using a fixed-point iteration approach with a fully asynchronous parallel sweeper, unstructured coarse-mesh finite difference, and a multi-timescale improved quasi-static method scheme. The implementation is applied to a multiphysics microreactor model, with a two transients: one initiated by a single heat-pipe failure and the other by the rotation of control drums. These examples demonstrate the ability of Griffin to tractably solve the seven-dimensional neutron transport equation with feedback.