Theoretical and numerical structure for unstable one-dimensional detonations
Theoretical and numerical structure for unstable one-dimensional detonations
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DOI：
10.1137/0151016
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发表时间：
1991-02
影响因子：
1.9
通讯作者：
A. Bourlioux;A. Majda;V. Roytburd
中科院分区：
文献类型：
--
作者：
A. Bourlioux;A. Majda;V. Roytburd
本文采用数值方法和渐近方法相结合的方法，研究了一维不稳定爆轰波的时空结构。发展了一种新的高分辨率数值计算不稳定爆轰的方法。该方法结合了分段抛物方法（PPM）与保守激波跟踪和自适应网格加密。一个新的非线性渐近理论的时空增长的不稳定性。这种渐近理论涉及到一个非经典的“霍普夫分岔”，因为共振声散射态的指数增长的空间交叉的虚轴，成为非线性特征模在一个复杂的自由边界问题的非线性双曲型方程。渐近理论和数值模拟之间的相互作用是用来阐明过渡边界附近的非线性稳定性的时空机制，特别是，定量定性的解释实验观察到的不稳定性...
The spatio-temporal structure of unstable detonations in a single space dimension is studied through a combination of numerical and asymptotic methods. A new high resolution numerical method for computing unstable detonations is developed. This method combines the piecewise parabolic method (PPM) with conservative shock tracking and adaptive mesh refinement. A new nonlinear asymptotic theory for the spatio-temporal growth of instabilities is also developed. This asymptotic theory involves a nonclassical “Hopf bifurcation”, because resonant acoustic scattering states with exponential growth in space cross the imaginary axis and become nonlinear eigenmodes in a complex free-boundary problem for a nonlinear hyperbolic equation. An interplay between the asymptotic theory and numerical simulation is used to elucidate the spatio-temporal mechanisms of nonlinear stability near the transition boundary; in particular, a quantitative-qualitative explanation is developed for the experimentally observed instabilities...