Number 1 pp. The closure problem for combustion waves arises when applying the method of matched asymptotic expansions for large activation energy to many nonsteady combustion problems.
Equations describing the first order correction involve the second order correction, and so on.
These terms can be scaled away for steady solutions, but when considering nonsteady propagation, they remain for any constant scaling of temperature. The closure problem refers to the fact that the equations must be solved at all orders before the leading order solution can be determined. One traditional approach to alleviate the problem is to truncate the series. While sacrificing the distinction between scales of temperature variation ahead of and behind the flame, these methods allow the replacement of the distributed reaction with a delta function reaction rate model. We present an alternative procedure which uses generalized matched asymptotic expansions and an associated truncation-like restriction to allow formulation of a model which retains the scales of temperature variation at the expense of a simple delta function interpretation of the model.