Abstract
We study nonlinear stability and instability of detonation waves through a dynamic model which includes nonlinear convection, chemical reaction, weak curvature effect and induction kinetics. The stability of the plane and the divergent detonation waves were established rigorously when there is no induction-zone. Furthermore, when the wave front has a small positive curvature and when there is an induction-zone behind the shock front, we captured dynamically unstable solutions through numerical simulations. The unstable solutions are accompanied by velocity fluctuations.
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Li, T. (1999). Stability and Instability of Detonation Waves. In: Jeltsch, R., Fey, M. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8724-3_15
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DOI: https://doi.org/10.1007/978-3-0348-8724-3_15
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