Many important scientific and engineering applications require a detailed analysis of complex systems with coupled fluid flow, thermal energy transfer, mass transfer and nonequilibrium chemical reactions. Currently, computer simulations of these complex reacting flow problems are limited to idealized systems in one or two spatial dimensions when coupled with a detailed, fundamental chemistry model. The goal of our research is to develop, analyze and implement advanced MP numerical algorithms that will allow high resolution 3D simulations with an equal emphasis on fluid flow and chemical kinetics modeling. In our research, we focus on the development of new, fully coupled, implicit solution strategies that are based on robust MP iterative solution methods.