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

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 $\gamma \to 1$, 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.

arXiv comment15 pages, no figures, submitted

References in corpus (1)

• High Mach number limit of one-dimensional piston problem for non-isentropic compressible Euler equations: Polytropic gas

Cited by in corpus (3)

• High Mach number limit of one-dimensional piston problem for non-isentropic compressible Euler equations: Polytropic gas
• Measure solutions of one-dimensional piston problem for compressible Euler equations of Chaplygin gas
• Hypersonic Similarity for the Two Dimensional Steady Potential Flow with Large Data