Numerical studies of the evolution of detonations

Some studies of the evolution of the shock-induced initiation of detonations are presented here. The aim is to examine the way that the dynamics and the chemistry of the system interact to produce detonation waves. Our present approach for constructing algorithms suitable for this type of flows is outlined, after a brief statement of the governing equations. A chemically-active flow governed by the reactive Euler equations, which has an exact solution, is used as a validation exercise. Various (previously loosely-connected) pieces of numerical and analytical work are brought together in lieu of a review, to set the scene for the multidimensional studies that follow. Two-dimensional flow is induced by a temperature perturbation ΔT of order ϵ (the dimensionless inverse activation energy), in an otherwise planar flowfield. The effect of small variations in ΔT on the ignition pattern is investigated by means of a series of numerical integrations. Analysis of the results gives some preliminary indications regarding the role of quasisteady structures during weak ignition.