Novel numerical techniques based upon Steger-Warming, Van Leer, and Roe-type flux splittings are presented in three-dimensional generalized coordinates for the Navier-Stokes equations governing flows out of chemical and thermal equilibrium. Attention is placed on convergence to steady-state solutions with fully coupled chemistry. Time integration schemes including explicit m-stage Runge-Kutta, implicit approximate-factorization, relaxation, and LU decomposition are investigated and compared in terms of residual reduction per unit of CPU time. Practical issues such as code vectorization and memory usage on modern supercomputers are discussed. © 1992 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.