Stability of Conical Shocks in the Three-Dimensional Steady Supersonic Isothermal Flows Past Lipschitz Perturbed Cones
Stability of Conical Shocks in the Three-Dimensional Steady Supersonic Isothermal Flows Past Lipschitz Perturbed Cones
复制标题
经过 Lipschitz 扰动锥体的三维稳态超音速等温流中圆锥激波的稳定性
DOI：
10.1137/20m1357962
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发表时间：
2020-08
影响因子：
2
通讯作者：
Zhang Yongqian
中科院分区：
文献类型：
--
作者：
Chen Gui Qiang G.;Kuang Jie;Zhang Yongqian
研究了顶角小于临界角的利普希茨摄动锥体在三维稳定超声速流动中的结构稳定性问题。所考虑的流动由轴对称势流的定常等温欧拉方程控制，使得方程包含一个奇异的几何源项。首先将激波稳定性问题表述为一个以前圆锥激波阵面为自由边界的初边值问题，然后在$BV$中建立了该问题全局熵解的存在性和渐近性。为了实现这一点，我们首先开发了一种改进的Glimm方案，通过自相似解作为构建块来构建近似解，以便与几何源项合并。然后，我们引入了基于弱波、强超前圆锥激波和自相似解之间的局部相互作用估计以及自相似解的中心变化估计的glimm型泛函。为了保证glimm型泛函的减小，在来流马赫数足够大时，通过对相互作用估计中的反射系数进行仔细的渐近分析，选择合适的权值。最后，在来流马赫数足够大、利普希茨摄动锥生成曲线斜率加权总变差足够小的条件下，我们建立了除弱波外，还存在强前锥激波阵面整体熵解的存在性。进一步证明了熵解渐近地逼近由流入流和圆锥边界的渐近切线决定的自相似解。
We are concerned with the structural stability of conical shocks in the three-dimensional steady supersonic flows past Lipschitz perturbed cones whose vertex angles are less than the critical angle. The flows under consideration are governed by the steady isothermal Euler equations for potential flow with axisymmetry so that the equations contain a singular geometric source term. We first formulate the shock stability problem as an initial-boundary value problem with the leading conical shock-front as a free boundary, and then establish the existence and asymptotic behavior of global entropy solutions in $BV$ of the problem. To achieve this, we first develop a modified Glimm scheme to construct approximate solutions via self-similar solutions as building blocks in order to incorporate with the geometric source term. Then we introduce the Glimm-type functional, based on the local interaction estimates between weak waves, the strong leading conical shock, and self-similar solutions, as well as the estimates of the center changes of the self-similar solutions. To make sure the decreasing of the Glimm-type functional, we choose appropriate weights by careful asymptotic analysis of the reflection coefficients in the interaction estimates, when the Mach number of the incoming flow is sufficiently large. Finally, we establish the existence of global entropy solutions involving a strong leading conical shock-front, besides weak waves, under the conditions that the Mach number of the incoming flow is sufficiently large and the weighted total variation of the slopes of the generating curve of the Lipschitz perturbed cone is sufficiently small. Furthermore, the entropy solution is shown to approach asymptotically the self-similar solution that is determined by the incoming flow and the asymptotic tangent of the cone boundary at infinity.
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影响因子：
2.4
作者：
Gui-Qiang G. Chen;David Wagner
通讯作者：
Gui-Qiang G. Chen;David Wagner
通过锥体的稳定超音速流的全局超音速圆锥激波：多变气体
影响因子：
2.4
作者：
崔大成;尹会成
通讯作者：
尹会成
经过多维楔块的稳定超音速流中跨音速激波的稳定性
影响因子：
1.7
作者：
Chen Gui-Qiang;Fang Beixiang
通讯作者：
Fang Beixiang
DOI：
10.1137/080712933
发表时间：
2009
期刊：
SIAM J. Math. Anal.
影响因子：
--
作者：
Gang Xu;Huicheng Yin
通讯作者：
Gang Xu;Huicheng Yin
影响因子：
64.8
作者：
M. Lighthill
通讯作者：
M. Lighthill