In rapid granular flows, particles interact vigorously with their neighbors through highly dissipative collisions. At present, there are no theories that adequately describe these flows. This study will extend methods from the kinetic theory of nonuniform gases to obtain a complete continuum theory for granular flows of identical, highly inelastic, smooth spheres. The theory will consist of balance equations that govern the variations of the relevant mean fields and constitutive relations that measure the rates at which these means are transferred throughout the flow. The statistical averaging required to derive the constitutive theory will be based upon a generalization of the Maxwellian velocity distribution that applies to systems of highly inelastic particles. When it is applied to homogeneous shear flows, for example, the theory's results will be in excellent agreement with the corresponding computer simulations. Methods of statistical averaging will be employed to derive boundary conditions for flows of identical spheres that interact, through highly inelastic collisions, with bumpy surfaces. These conditions will complement the general flow theory by ensuring that the fluxes of the flow properties relevant to highly inelastic systems are balanced at these boundaries.
