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Global NonIsentropic Rotational Supersonic Flows in a Semi-Infinite Divergent Duct
SIAM Journal on Mathematical Analysis ( IF 2 ) Pub Date : 2020-10-20 , DOI: 10.1137/20m1326453 Geng Lai
SIAM Journal on Mathematical Analysis ( IF 2 ) Pub Date : 2020-10-20 , DOI: 10.1137/20m1326453 Geng Lai
SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 5121-5154, January 2020.
Supersonic flows for the two-dimensional (2D) steady full Euler system are studied. We construct a global nonisentropic rotational supersonic flow in a semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the duct, and the state of the flow is given at the inlet of the duct. The solution is constructed by the method of characteristics. The main difficulty for the global existence is that a uniform a priori $C^1$ norm estimate of the solution is hard to obtain, especially when the solution tends to vacuum state. We derive a group of characteristic decompositions for the 2D steady full Euler system. Using these decompositions, we obtain uniform a priori estimates for the derivatives of the solution. A sufficient condition for the appearance of vacuum is also given. We show that if there is a vacuum then the vacuum is always adjacent to one of the walls, and the interface between gas and vacuum must be straight. The method used here also may be used to construct some other 2D steady nonisentropic rotational supersonic flows.
中文翻译:
半无限发散管中的整体非等熵旋转超音速流
SIAM数学分析杂志,第52卷,第5期,第5121-5154页,2020年1月。
研究了二维(2D)稳定全欧拉系统的超音速流动。我们在半无限发散管中构造了一个整体的非等熵旋转超声速流。流动满足管道壁上的滑动条件,并且流动状态在管道入口处给出。解决方案是通过特征方法构造的。整体存在的主要困难是,很难获得一个统一的先验$ C ^ 1 $范数估计值的溶液,尤其是当溶液趋于真空状态时。我们导出了二维稳定全欧拉系统的一组特征分解。使用这些分解,我们获得溶液导数的统一先验估计。还给出了出现真空的充分条件。我们表明,如果存在真空,则真空总是与壁之一相邻,并且气体与真空之间的界面必须是笔直的。这里使用的方法还可以用于构造其他一些2D稳态非等熵旋转超声速流。
更新日期:2020-10-26
Supersonic flows for the two-dimensional (2D) steady full Euler system are studied. We construct a global nonisentropic rotational supersonic flow in a semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the duct, and the state of the flow is given at the inlet of the duct. The solution is constructed by the method of characteristics. The main difficulty for the global existence is that a uniform a priori $C^1$ norm estimate of the solution is hard to obtain, especially when the solution tends to vacuum state. We derive a group of characteristic decompositions for the 2D steady full Euler system. Using these decompositions, we obtain uniform a priori estimates for the derivatives of the solution. A sufficient condition for the appearance of vacuum is also given. We show that if there is a vacuum then the vacuum is always adjacent to one of the walls, and the interface between gas and vacuum must be straight. The method used here also may be used to construct some other 2D steady nonisentropic rotational supersonic flows.
中文翻译:
半无限发散管中的整体非等熵旋转超音速流
SIAM数学分析杂志,第52卷,第5期,第5121-5154页,2020年1月。
研究了二维(2D)稳定全欧拉系统的超音速流动。我们在半无限发散管中构造了一个整体的非等熵旋转超声速流。流动满足管道壁上的滑动条件,并且流动状态在管道入口处给出。解决方案是通过特征方法构造的。整体存在的主要困难是,很难获得一个统一的先验$ C ^ 1 $范数估计值的溶液,尤其是当溶液趋于真空状态时。我们导出了二维稳定全欧拉系统的一组特征分解。使用这些分解,我们获得溶液导数的统一先验估计。还给出了出现真空的充分条件。我们表明,如果存在真空,则真空总是与壁之一相邻,并且气体与真空之间的界面必须是笔直的。这里使用的方法还可以用于构造其他一些2D稳态非等熵旋转超声速流。