This research addresses supercomputing aspects in reacting flows. It is well known that the success of computational fluid dynamics hinges on efficient numerical methods and data management on the supercomputer. This is particularly true when complicated physical phenomena such as turbulence, shock waves, and reacting flows are involved. The emphasis in this research will be placed on supercomputing aspects such as multigrid adaptive methods, unstructured grids, vector processing, and parallel processing. The best features of finite differences and finite element will be investigated, although emphasis is on finite elements due to an advantage in unstructured grids. With the most rigorous supercomputing capabilities available, our efforts will then be centered on evaluation and development of numerical strategies in dealing with widely disparate length and time scales typical of turbulence and reating flows. The end product is to achieve an enhanced understanding of the physics of turbulent flow phenomena in general and combustion of propulsion systems in particular.