Hypersonic limit of two‐dimensional steady compressible Euler flows passing a straight wedge
Hypersonic limit of two‐dimensional steady compressible Euler flows passing a straight wedge
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DOI：
10.1002/zamm.201800225
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发表时间：
2019-04
期刊：
影响因子：
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通讯作者：
Aifang Qu;Hairong Yuan;Qin Zhao
中科院分区：
文献类型：
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作者：
Aifang Qu;Hairong Yuan;Qin Zhao
我们提出了一个关于二维定常非等熵可压缩欧拉流通过直楔的高超音速极限问题。结果表明，当多方气体的绝热指数γ减小到1时，即将到来的均匀超声速流动的马赫数增大到无穷大。我们提出了一种形式的欧拉方程，这是有效的，如果未知数是Radon措施，并构建一个测量解决方案包含Dirac措施支持的表面上的楔形。证明了当γ→1时，楔体前方含有激波的可压缩Euler方程的解序列作为测度模糊地收敛于所构造的测度解.这证明了在二维直楔情况下高超音速气流通过障碍物的牛顿理论是正确的。这一结果也证明了在研究双曲型守恒律组边值问题时考虑一般测度解的必要性。
We formulate a problem on hypersonic limit of two‐dimensional steady non‐isentropic compressible Euler flows passing a straight wedge. It turns out that the Mach number of the upcoming uniform supersonic flow increases to infinity may be taken as that the adiabatic exponent γ of the polytropic gas decreases to 1. We propose a form of the Euler equations which is valid if the unknowns are Radon measures and construct a measure solution containing Dirac measures supported on the surface of the wedge. It is proved that as γ→1 , the sequence of solutions of the compressible Euler equations that contains a shock ahead of the wedge converges vaguely as measures to the measure solution constructed. This justifies the Newton theory of hypersonic flow passing obstacles in the case of two‐dimensional straight wedges. The result also demonstrates the necessity of considering general measure solutions in the study of boundary‐value problems of systems of hyperbolic conservation laws.