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Unsteady, three-dimensional, supersonic ow with nonequilibrium chemistry in a square channel with transverse hydrogen injection was numerically investigated. To this end, the concepts of large-eddy simulation were applied to a model supersonic combustion chamber using a three-dimensional solver of the compressible NavierStokes equations with chemical reactions developed by the present authors. The time-accurate computation was accelerated by an implicit method and implemented on a massively parallel computer. The results of the present three-dimensional simulation were analyzed with respect to their timewise behavior and compared, where applicable, with two-dimensional predictions and experimental data obtained by other investigators. NomenclatureA; B; C = Jacobian matrices e = total energy O F; O G; O H = ux vectors I = identity matrix J = Jacobian of the transformation k = turbulent kinetic energy L = limiter M = Mach number p = pressure Q = vector of state variables Re = Reynolds number S = source term T = temperature t = time U = velocity vector u; v; w = velocity components y C = wall distance 1 C = forward difference 1 ¡ = backward difference ² = dissipation of turbulent kinetic energy · = factor in MUSCL »;´; = body-tted coordinates ½ = density Subscripts i = index in x direction n s = number of species R = right v = viscous x = axial coordinate 0 = total quantity Superscripts n = timestep = transformed values ¡ = time averaged Presented as Paper 99-4902 at the 9th International Space Planes and