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arXiv · 1904.03360

Hypersonic limit of two-dimensional steady compressible Euler flows passing a straight wedge

Aifang Qu·Hairong Yuan·Qin Zhao
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Abstract

We formulated a problem on hypersonic limit of two-dimensional steady non-isentropic compressible Euler flows passing a straight wedge. It turns out that Mach number of the upcoming uniform supersonic flow increases to infinite may be taken as the adiabatic exponent $\gamma$ of the polytropic gas decreases to $1$. We proposed a form of the Euler equations which is valid if the unknowns are measures and constructed a measure solution contains Dirac measures supported on the surface of the wedge. It is proved that as $\gamma \to1$, the sequence of solutions of the compressible Euler equations that containing a shock ahead of the wedge converge vaguely as measures to the measure solution we constructed. This justified 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 studies of boundary-value problems of systems of hyperbolic conservation laws.

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Aifang Qu, Hairong Yuan, Qin Zhao. 2019-04-06. Hypersonic limit of two-dimensional steady compressible Euler flows passing a straight wedge. https://arxiv.org/abs/1904.03360

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