The implementation of a modular particle-continuum (MPC) numerical method is presented which solves the Navier-Stokes (NS) equations in regions of near-equilibrium and uses the direct simulation Monte Carlo (DSMC) method where the flow is in non-equilibrium. A mesh refinement procedure is described which allows the NS equations to be solved on a relatively coarse mesh using large implicit time-steps while the DSMC method is used in localized regions on a refined mesh. The MPC method accommodates a novel modular implementation which combines existing, state-of-the-art, DSMC and NS source codes, virtually un-modified, into a single modular code. Hypersonic flow over a 2D cylinder at various Mach numbers is simulated using DSMC, NS, and MPC methods and results are compared for accuracy. Added mesh refinement capability increases the efficiency of the MPC method which is able to reproduce DSMC flow field results for simple transitional flows up to 3 times faster while requiring half the memory. When applied to a mainly continuum flow, the MPC method reproduces non-equilibrium DSMC results in the near-wake region approximately 10 times faster than full DSMC simulation while using only 8% of the memory.