The data structures and overall algorithms of a newly developed 3-D direct simulationMonteCarlo (DSMC) program are outlined. The code employs an embedded 3-level Cartesian mesh, accompanied by a cut-cell algorithm to incorporate triangulated surface geometry into the adaptively refined Cartesian mesh. Such an approach enables decoupling of the surface mesh from the flow field mesh, which is desirable for near-continuum flows, flows with large density variation, and also for adaptive mesh refinement (AMR). Two separate data structures are proposed in order to separate geometry data from cell and particle information. The geometry data structure requires little memory so that each partition in a parallel simulation can store the entire mesh, potentially leading to better scalability and efficient AMR for parallel simulations. A simple and efficient AMR algorithm that maintains local cell size and time step consistent with the local mean-free-path and local mean collision time is detailed. The 3-level embedded Cartesian mesh combined with AMR allows increased flexibility for precise control of local mesh size and time-step, both vital for accurate and efficient DSMC simulation. Simulations highlighting the benefits of AMR and variable local time steps will be presented along with DSMC results for 3-D flows with large density variations.