Weak Shock Reflection

Hunter, John K.; Tesdall, Allen M.

doi:10.1007/978-94-017-0427-4_6

Cited by 22 publications

(38 citation statements)

References 19 publications

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“…The supersonic patches obtained in the solutions in [8,18,19] appeared to confirm Guderley's four wave solution. The patch indicates that it is plausible for an expansion fan to be an unobserved part of the observed three-shock confluence, since the flow must be supersonic for an expansion wave to occur.…”

Section: Introductionsupporting

confidence: 69%

“…The first indication that Guderley's proposed resolution might be essentially correct was contained in numerical solutions of shock reflection problems for the unsteady transonic small disturbance equations (UTSDE) in [8] and the compressible Euler equations in [18]. Solutions containing a supersonic patch embedded in the subsonic flow directly behind the triple point in a weak shock Mach reflection were presented there.…”

Section: Introductionmentioning

confidence: 99%

“…It was shown that the triple points with expansion fans observed numerically are consistent with theory and resolve the paradox. The term Guderley Mach reflection was chosen in [9] to name this new reflection pattern.…”

Section: Introductionmentioning

confidence: 99%

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Self-Similar Solutions for the Triple Point Paradox in Gasdynamics

Tesdall¹,

Sanders²,

Keyfitz³

2008

SIAM J. Appl. Math.

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We present numerical solutions of a two-dimensional Riemann problem for the compressible Euler equations that describes the Mach reflection of weak shock waves. High resolution finite volume schemes are used to solve the equations formulated in self-similar variables. We use extreme local grid refinement to resolve the solution in the neighborhood of an apparent but mathematically inadmissible shock triple point. The solutions contain a complex structure: instead of three shocks meeting in a single standard triple point, there is a sequence of triple points and tiny supersonic patches behind the leading triple point, formed by the reflection of weak shocks and expansion waves between the sonic line and the Mach shock. An expansion fan originates at each triple point, resolving the von Neumann triple point paradox.

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Section: Introductionsupporting

confidence: 69%

Section: Introductionmentioning

confidence: 99%

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Self-Similar Solutions for the Triple Point Paradox in Gasdynamics

Tesdall¹,

Sanders²,

Keyfitz³

2008

SIAM J. Appl. Math.

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“…In self-similar flow this would amount to non-uniqueness for an initial-value problem. Indeed, [6,7] has found a set of initial data for the 2d Euler equations (both isentropic and non-isentropic) that appears to have two solutions, one theoretical, the other clearly different and observed in all numerical calculations 16 For isentropic Euler, a rigorous proof of a different non-uniqueness example has recently been proposed [19]. 13 also referred to as mechanical equilibrum criterion in some contexts 14 Even in Euler flow it applies only for large M 1 , for example M 1 > 2.2... for γ = 7/5.…”

Section: Other Remarksmentioning

confidence: 99%

“…13 also referred to as mechanical equilibrum criterion in some contexts 14 Even in Euler flow it applies only for large M 1 , for example M 1 > 2.2... for γ = 7/5. 15 stability under perturbations to the initial data 16 In addition it is shown that the Godunov scheme can converge to either solution, depending on the grid. However, both results depend strongly on vorticity; uniqueness for the potential flow Cauchy problem is still expected and hysteresis is unlikely except as a transient phenomenon.…”

Section: Other Remarksmentioning

confidence: 99%

Counterexamples to the Sonic Criterion

Elling

2008

Arch Rational Mech Anal

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We consider self-similar (pseudo-steady) shock reflection at an oblique wall. There are three parameters: wall corner angle, Mach number, angle of incident shock. Ever since Ernst Mach discovered the irregular reflection named after him, it has been an open problem to predict precisely for what parameters the reflection is regular. Three conflicting proposals, the detachment, sonic and von Neumann criteria, have been studied extensively without a clear result.We demonstrate that the sonic criterion is not correct. We consider polytropic potential flow and prove that there is an open nonempty set of parameters that admit a global regular reflection with a reflected shock that is transonic.We also provide a clear physical reason: the flow type (sub-or supersonic) is not decisive; instead the reflected shock type (weak or strong) determines whether structural perturbations decay towards the reflection point.1 equation of state p = (γ − 1)ρe, e internal energy per mass, γ ∈ (1, ∞)

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Regular reflection in potential flow and the sonic criterion

Elling

2007

Proc Appl Math and Mech

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We study the classical problem of self-similar reflection of shocks at a ramp, modeled by potential flow with γ-law pressure. Depending on corner angle θ and upstream Mach number MI , either regular (RR) or Mach reflections occur. There are several conflicting transition criteria predicting the corner angle at which the type of reflection changes. We show that in some cases, in particular MI = 1 and γ = 5/3, an exact RR solution exists for all θ specified by the sonic criterion. Thus all weaker criteria are false.

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Weak Shock Reflection

Cited by 22 publications

References 19 publications

Self-Similar Solutions for the Triple Point Paradox in Gasdynamics

Self-Similar Solutions for the Triple Point Paradox in Gasdynamics

Counterexamples to the Sonic Criterion

Regular reflection in potential flow and the sonic criterion

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