Unsteady one-dimensional flows of chemically reacting gas: Group analysis and solution of a strong explosion problem

Abstract

This work analyzes a system describing the motion of a two-component chemically reacting gas. We provide a complete group classification, enabling the identification of self-similar solutions to address the strong explosion problem. This approach allows for the examination of real Arrhenius-type chemical kinetics. Instead of solving a complex system of determining equations for admitted Lie groups, we employ an alternative method based on the system’s equivalence transformations. The strong explosion problem is studied, and, as in the classical case, the solution is reduced to integrating a system of ordinary differential equations in self-similar variables, which differ from the classical case. The results are illustrated with visual representations.