论文标题
在3-D轴对称圆柱喷嘴中稳定的Euler流动的透射冲击的可接受位置
On Admissible Positions of Transonic Shocks for Steady Euler Flows in a 3-D Axisymmetric Cylindrical Nozzle
论文作者
论文摘要
本文涉及在3-D轴对称圆柱喷嘴中存在稳定欧拉流的跨音速冲击，该喷嘴由欧拉方程控制，其壁上的滑动壁上的滑动边界条件和出口处的接收器压力。从数学上讲，它可以作为自由边界问题进行配合，而冲击阵线是要确定的自由边界。在处理自由边界问题时，关键点之一是确定冲击战线的位置。为此，将提出线性化的Euler系统的自由边界问题，其解决方案给出了冲击前线的初始近似位置。与2-D情况相比，由于沿对称轴的额外的0阶项和奇异性，出现了新的困难。将进行新的观察和仔细的分析，以克服这些困难。一旦获得了初始近似，就可以执行非线性迭代方案，该方案将其收敛到跨音速冲击解决方案。
This paper concerns with the existence of transonic shocks for steady Euler flows in a 3-D axisymmetric cylindrical nozzle, which are governed by the Euler equations with the slip boundary condition on the wall of the nozzle and a receiver pressure at the exit. Mathematically, it can be formulated as a free boundary problem with the shock front being the free boundary to be determined. In dealing with the free boundary problem, one of the key points is determining the position of the shock front. To this end, a free boundary problem for the linearized Euler system will be proposed, whose solution gives an initial approximating position of the shock front. Compared with 2-D case, new difficulties arise due to the additional 0-order terms and singularities along the symmetric axis. New observation and careful analysis will be done to overcome these difficulties. Once the initial approximation is obtained, a nonlinear iteration scheme can be carried out, which converges to a transonic shock solution to the problem.
