Abstract
The problem of the numerical modeling of unsteady flame propagation with large amounts of exothermic heat release has been addressed through the use of a model equation which contains many of the important nonlinearities and difficulties in the problem. The model equation has been solved for a significant variation in Damköhler number with a variety of conventional and new finite-difference procedures. One of the new procedures used was an adaptive grid method which places node points in the region of large temperature gradients where they are necessary for a proper simulation of the phenomena. This adaptive grid procedure does have significant advantages over conventional second and fourth order uniform grid methods for many aspects of the problem. It has been found that conventional methods with relatively few node points are inadequate for flames with high Damköhler number, because of the fact that too few nodes are located in the flame. Further refinement of the adaptive grid method seems feasible, but even in the present form it represents a significant improvement over conventional techniques.
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