Simulations of pulsating one-dimensional detonations with true fifth order accuracy
Simulations of pulsating one-dimensional detonations with true fifth order accuracy
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DOI：
10.1016/j.jcp.2005.08.013
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发表时间：
2006-03
期刊：
影响因子：
--
通讯作者：
A. Henrick;T. Aslam;J. M. Powers
中科院分区：
文献类型：
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作者：
A. Henrick;T. Aslam;J. M. Powers
一种新的，高精度的数值格式的基础上，激波拟合耦合五阶空间和时间离散的经典非定常爆轰问题产生前所未有的精度的解决方案。一维反应欧拉方程的理想气体的理想混合物的热量，其反应是由单步不可逆的Arrhenius动力学描述的解决了一系列的计算，其中的活化能是不同的。与几乎所有已知的模拟这个问题，收敛速度不大于第一阶的空间和时间网格细化，本方法收敛速度与五阶精度的空间和时间离散化方案一致。这种高精度使得能够更精确地验证已知结果和预测迄今未知的现象。五个有效数字，该计划忠实地恢复稳定边界，增长率和波数预测的一个独立的线性稳定性理论在稳定和弱不稳定的政权。随着激活能的增加，一系列的倍周期事件的预测，系统经历了一个过渡到混沌。与非线性动力学的一般理论相一致，分叉点被认为以Feigenbaum常数为4.66±0.09的速率收敛，与真实值4.669201非常接近。随着活化能的进一步增加，域被确定，在该系统中经历了从混沌状态的过渡回到一个其极限环的特征在于由少量的非线性振荡模式。这一结果与其他非线性动力学系统的行为是一致的，但在爆轰动力学中通常不考虑。计算了各种渐近稳定极限环的周期和平均爆速。这种脉动爆轰的平均速度被认为是略大于查普曼-茹盖速度。
A novel, highly accurate numerical scheme based on shock-fitting coupled with fifth order spatial and temporal discretizations is applied to a classical unsteady detonation problem to generate solutions with unprecedented accuracy. The one-dimensional reactive Euler equations for a calorically perfect mixture of ideal gases whose reaction is described by single-step irreversible Arrhenius kinetics are solved in a series of calculations in which the activation energy is varied. In contrast with nearly all known simulations of this problem, which converge at a rate no greater than first order as the spatial and temporal grid is refined, the present method is shown to converge at a rate consistent with the fifth order accuracy of the spatial and temporal discretization schemes. This high accuracy enables more precise verification of known results and prediction of heretofore unknown phenomena. To five significant figures, the scheme faithfully recovers the stability boundary, growth rates, and wave-numbers predicted by an independent linear stability theory in the stable and weakly unstable regime. As the activation energy is increased, a series of period-doubling events are predicted, and the system undergoes a transition to chaos. Consistent with general theories of non-linear dynamics, the bifurcation points are seen to converge at a rate for which the Feigenbaum constant is 4.66±0.09, in close agreement with the true value of 4.669201…. As activation energy is increased further, domains are identified in which the system undergoes a transition from a chaotic state back to one whose limit cycles are characterized by a small number of non-linear oscillatory modes. This result is consistent with behavior of other non-linear dynamical systems, but not typically considered in detonation dynamics. The period and average detonation velocity are calculated for a variety of asymptotically stable limit cycles. The average velocity for such pulsating detonations is found to be slightly greater than the Chapman–Jouguet velocity.