For the past several years, à comprehensive research has been under way to de. fine a viable air-breathing propulsion system for hypersonic flight applications. en this fight regime, a supersonic combustion ramjet (scramjet) engine becomes attractive. fundamental research into the design of the supersonie combustion process has been persued at sheffield university for many years. however, this research has necessarily been experimental because of the complex nature of the combustor flow field, which is highly three-dimensional, turbulent, and has complex shock-wave interactions. it also involves strong shock-wave/boundary-layer interactions which result in separated regions. however, with the availability of large-storage, high-speed computers and advanced numerical algorithms, it is now feasible to calculate many complex twoand three-dimensional problems that could not be calculated previously. this thesis describes a numerical study in supersonic reacting flows involving the spark3d numerical subroutines, which use the full reynolds averaged navier. stokes equations and à chemistry model in conservation form as the governing equations. the purpose in this study is to develop a fully three-dimensional code for analysing actual combustor configurations, an emerging problem however, is the generation of grid systems on which sojutions can be obtained when there are complex boundary geometries. an algebraic grid generation technique [13] is presented in this thesis. the grid generation technique is called the "twoboundary technique " and is applicable in two and three dimensions. it is based on algebraically defining two distinct non-intersecting boundaries of a flow domain and joining the boundaries with à connection function which is proposed here to be linear. control of the distribution of the grid in the physical domain is achieved by embeding "control functions " which redistribute the uniform grid of the computational domain and concentrate or disperse the grid in the physical domain. coupled with the spark3d-code the "two-boundary technique ? is demonstrated to be viable for grid generation associated with computing complex supersonic laminar or turbulent chemically reacting flow fields. in the case of turbulent flows, an algebraic, two-layer, eddy-viscosity model of baldwin and lomax [9] is used to estimate the turbulent viscosity. the code is first checked against two test cases for which detailed experimental data are available. then the generalized chemistry version of the spark3d-code including the simulation of mixing, chemically reacting, h2-air flow is used to calculate the scramjet flow field experiment performed at the university of sheffield. finally two ramp fuel injector configurations are analysed with more emphasis on the mixing.