In response to the global SARS-CoV-2 transmission pandemic, Sandia National Laboratories Rapid Lab-Directed Research and Development COVID-19 initiative has deployed a multi-physics, droplet-laden, turbulent low-Mach simulation tool to model pathogen-containing water droplets that emanate from synthetic human coughing and breathing. The low-Mach turbulent large-eddy simulation-based Eulerian/point-particle Lagrangian methodology directly couples mass, momentum, energy, and species to capture droplet evaporation physics that supports the ability to distinguish between droplets that deposit and those that persist in the environment. The cough mechanism is modeled as a pulsed spray with a prescribed log-normal droplet size distribution. Simulations demonstrate direct droplet deposition lengths in excess of three meters while the persistence of droplet nuclei entrained within a buoyant plume is noted. Including the effect of protective barriers demonstrates effective mitigation of large-droplet transport. For coughs into a protective barrier, jet impingement and large-scale recirculation can drive droplets vertically and back toward the subject while supporting persistence of droplet nuclei. Simulations in quiescent conditions demonstrate droplet preferential concentrations due to the coupling between vortex ring shedding and the subsequent advection of a series of three-dimensional rings that tilt and rise vertically due to a misalignment between the initial principle vortex trajectory and gravity. These resolved coughing simulations note vortex ring formation, roll-up and breakdown, while entraining droplet nuclei for large distances and time scales.