On the Two-Dimensional Gas Expansion for Compressible Euler Equations
On the Two-Dimensional Gas Expansion for Compressible Euler Equations
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DOI：
10.1137/s0036139900361349
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Jiequan Li
中科院分区：
文献类型：
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作者：
Jiequan Li
我们研究了二维非定常膨胀的无粘多向气体的问题，它可以解释为一个楔形坝的崩塌，其中含有水，最初以匀速。我们用等熵欧拉方程来模拟这个问题。流是准平稳的，在初始为无旋时，利用矢状变换在状态空间中用二阶偏微分方程来描述它。进一步，将该方程简化为一个由三个非齐次源项的偏微分方程组成的线性退化系统。这些性质被用来证明当楔形气体膨胀到真空中时，流动是全局平滑的，并分析了在四个平面稀薄波的相互作用中可能出现激波。
We investigate the problem of two-dimensional, unsteady expansion of an inviscid, polytropic gas, which can be interpreted as the collapse of a wedge-shaped dam containing water initially with a uniform velocity. We model this problem by isentropic Euler equations. The flow is quasi-stationary, and using hodograph transform, we describe it by a partial differential equation of second order in the state space if it is irrotational initially. Furthermore, this equation is reduced to a linearly degenerate system of three partial differential equations with inhomogeneous source terms. These properties are used to prove that the flow is globally smooth when a wedge of gas expands into a vacuum, and to analyze that shocks may appear in the interaction of four planar rarefaction waves.