Structural Stability of the Transonic Shock Problem in a Divergent Three-Dimensional Axisymmetric Perturbed Nozzle
Structural Stability of the Transonic Shock Problem in a Divergent Three-Dimensional Axisymmetric Perturbed Nozzle
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DOI：
10.1137/20m1318869
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发表时间：
2019-08
期刊：
影响因子：
--
通讯作者：
S. Weng;Chunjing Xie;Z. Xin
中科院分区：
文献类型：
--
作者：
S. Weng;Chunjing Xie;Z. Xin
本文证明了具有旋流速度的三维轴对称Euler方程组在来流、喷管边界和出口压力扰动下的跨音速激波的结构稳定性。与已有的跨音速激波稳定性研究结果相比，有旋轴对称流动的主要困难之一是激波面与喷管边界交点附近的角奇异性和轴附近的人工奇异性同时出现。本文分析的关键之一是引入了一个可逆的拉格朗日变换，它可以拉直整个喷管中的流线，并有助于显式地表示输运方程的解。
In this paper, we prove the structural stability of the transonic shocks for three dimensional axisymmetric Euler system with swirl velocity under the perturbations for the incoming supersonic flow, the nozzle boundary, and the exit pressure. Compared with the known results on the stability of transonic shocks, one of the major difficulties for the axisymmetric flows with swirls is that corner singularities near the intersection point of the shock surface and nozzle boundary and the artificial singularity near the axis appear simultaneously. One of the key points in the analysis for this paper is the introduction of an invertible Lagrangian transformation which can straighten the streamlines in the whole nozzle and help to represent the solutions of transport equations explicitly.