The Bukiet-Jones Theory of Weak Detonation Waves in Curvilinear Geometry

Abstract

Front tracking is a numerical method which uses exact mathematical knowledge of idealized solution singularities within the computational process. This fact is typical of a broadly based scientific motivation for the study of nonlinear waves, wave interactions and Riemann problems in one and higher dimensions. Such a study is pertinent for a variety of physical systems, including oil reservoirs, real materials with realistic equation of state and constitute relations, chemically reactive fluids and plasmas.In this note, we report on a recent results of J. Jones in formulating and analyzing model equations to understand qualitatively and quantitatively (to first order) the effect of curvature on an expanding detonation wave front and the validation by numerical methods of the asymptotic correctness of this theory by B. Bukiet. These results are a necessary input to the front tracking method.