TY - JOUR
T1 - Complex dynamics generated by a sharp interface model of self-propagating high-temperature synthesis
AU - Frankel, M.
AU - Roytburd, V.
AU - Sivashinsky, G.
PY - 1998/12
Y1 - 1998/12
N2 - This paper presents results of a numerical study of a free-interface problem modelling self-propagating high-temperature synthesis (solid combustion) in a one-dimensional infinite medium. Evolution of the free interface exhibits a remarkable range of dynamical scenarios such as finite and infinite sequences of period doubling; the latter leading to chaotic oscillations, reverse sequences and infinite period bifurcation that may replace the supercritical Hopf bifurcation for some interface kinetics. Solutions were verified by using different numerical methods, including reduction to an integral equation for which convergence to the solutions has been demonstrated rigorously. Therefore, the ability of the free-interface model to generate the dynamical scenarios observed previously in models with a distributed reaction rate should be regarded as firmly established.
AB - This paper presents results of a numerical study of a free-interface problem modelling self-propagating high-temperature synthesis (solid combustion) in a one-dimensional infinite medium. Evolution of the free interface exhibits a remarkable range of dynamical scenarios such as finite and infinite sequences of period doubling; the latter leading to chaotic oscillations, reverse sequences and infinite period bifurcation that may replace the supercritical Hopf bifurcation for some interface kinetics. Solutions were verified by using different numerical methods, including reduction to an integral equation for which convergence to the solutions has been demonstrated rigorously. Therefore, the ability of the free-interface model to generate the dynamical scenarios observed previously in models with a distributed reaction rate should be regarded as firmly established.
UR - http://www.scopus.com/inward/record.url?scp=0011372814&partnerID=8YFLogxK
U2 - 10.1088/1364-7830/2/4/008
DO - 10.1088/1364-7830/2/4/008
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AN - SCOPUS:0011372814
SN - 1364-7830
VL - 2
SP - 479
EP - 496
JO - Combustion Theory and Modelling
JF - Combustion Theory and Modelling
IS - 4
ER -