Lower-upperscheme for chemically reacting flow with finite rate chemistry

A fourth-order shock-capturing scheme hasbeen developed for steady-state and time-accurate simulationof chemically reacting flows with finite rate chemical kinetics. A diagonal algorithm anda local implicit technique are presented to removethe stiffness of chemical reaction and to achieve high computation efficiency. A fully implicit codeis obtained by combining the presentalgorithm with the lower-upper scheme. The validity of this code is demonstrated by calculating the unsteady shocks in an inviscid supersonic duct and by comparingthe results with the previous calculation. Then the code is used to calculate the ignition of a premixed hydrogen/air reacting flow in a ramped duct and nonpremixed hydrogen/air streams as well as nonpremixed methane/air streams in a supersonic mixing layer. The efficiency androbustness of the present scheme are shown through these numerical simulations.