The generalized riemann problem for a scalar nonconvex combustion model—the perturbation on initial binding energy

Abstract

In this article, we study the generalized Riemann problem for a scalar non-convex Chapman-Jouguet combustion model in a neighborhood of the origin (t > 0) on the (x, t) plane. We focus our attention to the perturbation on initial binding energy. The solutions are obtained constructively under the entropy conditions. It can be found that the solutions are essentially different from the corresponding Riemann solutions for some cases. Especially, two important phenomena are observed: the transition from detonation to deflagration followed by a shock, which appears in the numerical simulations [7, 27]; the transition from deflagration to detonation (DDT), which is one of the core problems in gas dynamic combustion.