Three-Dimensional Steady Supersonic Euler Flow Past a Concave Cornered Wedge with Lower Pressure at the Downstream

Qu, Aifang; Xiang, Wei

doi:10.1007/s00205-017-1197-x

Cited by 20 publications

(10 citation statements)

References 28 publications

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“…we solve θ − , which is negative, hence k b = tan θ − and we find the downstream state U − in (18). Then k 1 = λ 3 (U + ) and k 2 = λ 3 (U − ).…”

Section: 1mentioning

confidence: 95%

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Stability of transonic jets with strong rarefaction waves for two-dimensional steady compressible Euler system

Ding¹,

Yuan²

2018

Discrete &Amp; Continuous Dynamical Systems - A

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We study supersonic flow past a convex corner which is surrounded by quiescent gas. When the pressure of the upstream supersonic flow is larger than that of the quiescent gas, there appears a strong rarefaction wave to rarefy the supersonic gas. Meanwhile, a transonic characteristic discontinuity appears to separate the supersonic flow behind the rarefaction wave from the static gas. In this paper, we employ a wave front tracking method to establish structural stability of such a flow pattern under non-smooth perturbations of the upcoming supersonic flow. It is an initial-value/free-boundary problem for the two-dimensional steady non-isentropic compressible Euler system. The main ingredients are careful analysis of wave interactions and construction of suitable Glimm functional, to overcome the difficulty that the strong rarefaction wave has a large total variation. 2010 Mathematics Subject Classification. Primary: 35L50, 35L65, 35Q31, 35R35; Secondary: 76N10.

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“…we solve θ − , which is negative, hence k b = tan θ − and we find the downstream state U − in (18). Then k 1 = λ 3 (U + ) and k 2 = λ 3 (U − ).…”

Section: 1mentioning

confidence: 95%

“…in [6]. There are also some results on transonic characteristic discontinuities for three-dimensional steady compressible Euler system, see [20,18].…”

mentioning

confidence: 99%

Stability of transonic jets with strong rarefaction waves for two-dimensional steady compressible Euler system

Ding¹,

Yuan²

2018

Discrete &Amp; Continuous Dynamical Systems - A

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“…Actually, we show that the non-constant irrotational flow will generally blow up in the semi-infinitely long flat nozzle in the Appendix (see Theorem A.1). The problem of the supersonic flow in nozzles is different from the problem of supersonic flow past a solid wall (see in [14,33]), or the local stability of straight contact discontinuity without boundary (see in [40,41]), for which the decay estimates are expected or there is no reflection on the characteristics. So far almost all the results on the supersonic flow in nozzles are about the nozzles with special structure, for example, the expanding nozzles.…”

Section: Introductionmentioning

confidence: 99%

Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite nozzle

Huang

Kuang

Wang

et al. 2019

Journal of Differential Equations

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In this paper, we study the stability of supersonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle of varying cross-sections. We formulate the problem as an initial-boundary value problem with the contact discontinuity as a free boundary. To deal with the free boundary value problem, we employ the Lagrangian transformation to straighten the contact discontinuity and then the free boundary value problem becomes a fixed boundary value problem. We develop an iteration scheme and establish some novel estimates of solutions for the first order of hyperbolic equations on a cornered domain. Finally, by using the inverse Lagrangian transformation and under the assumption that the incoming flows and the nozzle walls are smooth perturbations of the background state, we prove that the original free boundary problem admits a unique weak solution which is a small perturbation of the background state and the solution consists of two smooth supersonic flows separated by a smooth contact discontinuity.2010 Mathematics Subject Classification. 35B07, 35B20, 35D30; 76J20, 76L99, 76N10.

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“…For the one dimensional Euler equations, the low Mach number limit has been proved under the B.V. space in [7]. For other related fluid models and problems, see [5,11,22,26,27,30,31,33,34,36] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Low Mach Number Limit of Steady Euler Flows in Multi-Dimensional Nozzles

Wang

Xiang

2019

Preprint

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In this paper, we consider the steady irrotational Euler flows in multidimensional nozzles. The first rigorous proof on the existence and uniqueness of the incompressible flow is provided. Then, we justify the corresponding low Mach number limit, which is the first result of the low Mach number limit on the steady Euler flows. We establish several uniform estimates, which does not depend on the Mach number, to validate the convergence of the compressible flow with extra force to the corresponding incompressible flow, which is free from the extra force effect, as the Mach number goes to zero. The limit is on the Hölder space and is unique. Moreover, the convergence rate is of order ε 2 , which is higher than the ones in the previous results on the low Mach number limit for the unsteady flow.

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Three-Dimensional Steady Supersonic Euler Flow Past a Concave Cornered Wedge with Lower Pressure at the Downstream

Cited by 20 publications

References 28 publications

Stability of transonic jets with strong rarefaction waves for two-dimensional steady compressible Euler system

Stability of transonic jets with strong rarefaction waves for two-dimensional steady compressible Euler system

Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite nozzle

Low Mach Number Limit of Steady Euler Flows in Multi-Dimensional Nozzles

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