Formation of wrinkles in outwardly propagating flames.
Formation of wrinkles in outwardly propagating flames.
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向外传播的火焰中形成皱纹。
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
Lima
中科院分区：
文献类型：
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作者：
Rahibe;Aubry;Sivashinsky;Lima
Filyand，Sivashinsky和Frankel [Physica D 72，110（1994）]提出的描述向外加速火焰动力学的偏微分方程的数值积分。Filyand，Sivashinsky和Frankel报告的计算结果得到证实：随着时间的增加，重复形成的尖点，以及快速（幂律）的平均火焰半径的扩张，观察。然而，确定不变的子空间的方程表明，即使当初始条件属于这样的子空间，数值舍入误差是负责这些子空间以外的解决方案的游览。在傅立叶空间中，这对应于随着时间增加而增长的伪傅立叶模式的生成。这种计算误差在这里由一个过滤器控制，该过滤器在每个时间步强制解停留在不变子空间内。我们的过滤模拟的结果是非常相似的，从未过滤的积分，表明尖点的形成和快速加速的火焰前锋是独立的虚假傅立叶模式的增长。这种动态和精确的极点解的方程（其中极点的数量是固定的）之间的连接进行了研究。发现后者是不稳定的，而更复杂的（稳定的）动力学由连续的不稳定性组成，通过这些不稳定性，火焰锋在接近（2 {ital N}+3）极点解之前紧密地遵循（2 {ital N}+1）极点解。这些迁移是负责形成新的尖点和快速幂律加速的平均锋。«少
Numerical integrations of the partial differential equation proposed by Filyand, Sivashinsky, and Frankel [Physica D 72, 110 (1994)] to describe the dynamics of outward accelerating flames are presented. The computational results reported by Filyand, Sivashinsky, and Frankel are confirmed: as time increases, a repetitive formation of cusps, as well as a rapid (power-law) expansion of the mean flame radius, are observed. However, the identification of invariant subspaces for the equation shows that even when the initial condition belongs to such subspaces, numerical round-off errors are responsible for excursions of the solution outside these subspaces. In Fourier space, this corresponds to the generation of spurious Fourier modes that grow as time increases. This computational error is controlled here by a filter that forces the solution, at each time step, to stay inside the invariant subspaces. The results of our filtered simulations are very similar to those resulting from unfiltered integrations, showing that both the formation of cusps and the rapid acceleration of the flame front are independent of the growth of spurious Fourier modes. The connection between such dynamics and exact pole solutions of the equation (in which the number of poles is fixed) is investigated. It is found that themore » latter are unstable and the more complicated (stable) dynamics consists of successive instabilities through which the flame front closely follows a (2{ital N}+1)-pole solution before approaching a (2{ital N}+3)-pole solution. These migrations are responsible for both the formation of new cusps and the rapid power-law acceleration of the mean front.« less