An isotropic local mesh refinement technique for unstructured meshes is presented. The present work pertains to inviscid, steady, supersonic internal flows contained in a channel configuration. A density-based mesh refinement sensor function is used to identify regions in the mesh for refinement. A face-cell finite-volume method, permitting dynamic changes to mesh connectivity, is employed in the mesh refinement strategy. The AUSM+ convection scheme is used to compute the interface numerical flux using Mach number and pressure splitting functions. The present method is capable of recursive multi-level mesh adaption. Local mesh refinement equivalent to 64 and 256 times the coarse mesh resolution can be obtained using four and five levels of refinement, respectively. Results for two popular supersonic channel test cases are presented: Mach 1.4 flow over a 4% thick circular arc bump, and Mach 2.0 flow over a 10° compression ramp. The effort associated with the mesh refinement of the bump case accounts for only 4.6% of the total simulation time. For the ramp case, a factor of 4.2 for memory storage requirements and 7.7 for simulation time is required to obtain an equivalent uniform fine mesh solution.