The advent of super computers has brought us closer to effective numerical models of three-dimensional reacting flows. However, we are not there yet, especially in those realistic situations where the chemical kinetics are complex, and the grid size requirements are many. Only simplified flows (especially those reducing kinetics to one reaction) have been calculated. The originality of the asymptotic method developed by Williams is that he considers those special flame flows where some terms in the representative equations can be eliminated or linearized, thus lending themselves to closed form solutions. These solutions serve two purposes: a. They give a physical insight into those flows where the chemical constants happen to be in the range required for asymptotic representation. b. They give a reliable check for the more general numerical programs which will be eventually used for more complicated cases by the larger computers of the future: by entering the same properties in the numerical program as were considered for the asymptotic solution, the results should be identical. This form of check has proved to be essential in current large fluid dynamics numerical programs.
