Analytical reconsideration of the von Neumann paradox in the reflection of a shock wave over a wedge

2008 ◽  
Vol 20 (4) ◽  
pp. 046101 ◽  
Author(s):  
Eugene I. Vasilev ◽  
Tov Elperin ◽  
Gabi Ben-Dor
Keyword(s):  
Shock Wave ◽  
Von Neumann ◽  
Von Neumann Paradox

Examination of the von Neumann paradox for a weak shock wave

1995 ◽  
Vol 17 (1) ◽  
pp. 13-25 ◽  
Author(s):  
Susumu Kobayashi ◽  
Takashi Adachi ◽  
Tateyuki Suzuki
Keyword(s):  
Shock Wave ◽  
Weak Shock ◽  
Weak Shock Wave ◽  
Von Neumann ◽  
Von Neumann Paradox

Reconsideration of the So-Called von Neumann Paradox in the Reflection of a Shock Wave over a Wedge

2007 ◽  
Vol 566 ◽  
pp. 1-8
Author(s):  
Eugene I. Vasilev ◽  
Tov Elperin ◽  
Gabi Ben-Dor
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Triple Point ◽  
Mach Reflection ◽  
Weak Shock ◽  
Weak Shock Wave ◽  
Plane Shock ◽  
Von Neumann ◽  
Von Neumann Paradox ◽  
Guderley Reflection

Numerous experimental investigations on the reflection of plane shock waves over straight wedges indicated that there is a domain, frequently referred to as the weak shock wave domain, inside which the resulted wave configurations resemble the wave configuration of a Mach reflection although the classical three-shock theory does not provide an analytical solution. This paradox is known in the literature as the von Neumann paradox. While numerically investigating this paradox Colella & Henderson [1] suggested that the observed reflections were not Mach reflections but another reflection, in which the reflected wave at the triple point was not a shock wave but a compression wave. They termed them it von Neumann reflection. Consequently, based on their study there was no paradox since the three-shock theory never aimed at predicting this wave configuration. Vasilev & Kraiko [2] who numerically investigated the same phenomenon a decade later concluded that the wave configuration, inside the questionable domain, includes in addition to the three shock waves a very tiny Prandtl-Meyer expansion fan centered at the triple point. This wave configuration, which was first predicted by Guderley [3], was recently observed experimentally by Skews & Ashworth [4] who named it Guderley reflection. The entire phenomenon was re-investigated by us analytically. It has been found that there are in fact three different reflection configurations inside the weak reflection domain: • A von Neumann reflection – vNR, • A yet not named reflection – ?R, • A Guderley reflection – GR. The transition boundaries between MR, vNR, ?R and GR and their domains have been determined analytically. The reported study presents for the first time a full solution of the weak shock wave domain, which has been puzzling the scientific community for a few decades. Although the present study has been conducted in a perfect gas, it is believed that the reported various wave configurations, namely, vNR, ?R and GR, exist also in the reflection of shock waves in condensed matter.

Von Neumann reflection of underwater shock wave

1999 ◽  
Vol 85 (1-3) ◽  
pp. 48-51 ◽  
Author(s):  
Y Nadamitsu ◽  
Z.Y Liu ◽  
M Fujita ◽  
S Itoh
Keyword(s):  
Shock Wave ◽  
Underwater Shock Wave ◽  
Von Neumann ◽  
Underwater Shock

On von Neumann reflection of shock wave in condensed matter

1998 ◽  
Author(s):  
S. Itoh ◽  
Y. Natamitsu ◽  
Z. Y. Liu ◽  
M. Fujita
Keyword(s):  
Shock Wave ◽  
Condensed Matter ◽  
Von Neumann

ATTENUATION OF SPURIOUS OSCILLATIONS IN THE NUMERICAL CAPTURE OF SHOCK WAVES

2006 ◽  
Vol 17 (10) ◽  
pp. 1403-1413
Author(s):  
D. PORTES ◽  
H. RODRIGUES ◽  
S. B. DUARTE
Keyword(s):  
Shock Wave ◽  
Continuous Solution ◽  
Artificial Viscosity ◽  
Plane Shock ◽  
Hydrodynamic Equations ◽  
Von Neumann ◽  
One Dimensional ◽  
First Derivative ◽  
Spurious Oscillations ◽  
Steady Plane

Artificial viscosity is often expressed as a superposition of linear and quadratic terms in the first derivative of the velocity field. In trying to find a continuous solution for the hydrodynamic equations, we propose an alternative one-term artificial viscosity which is a linear form of the derivative of the specific volume. It is shown that this artificial viscosity is able to capture the profile of the steady plane shock wave, largely removing the non-physical oscillations originated by the artificial viscosity of von Neumann and Richtmyer. Analytical and numerical calculations for one-dimensional shock using both artificial viscosities are compared.

Non-self-similar characteristics of weak Mach reflection: the von Neumann paradox

2004 ◽  
Vol 35 (4) ◽  
pp. 275-286 ◽  
Author(s):  
Susumu Kobayashi ◽  
Takashi Adachi ◽  
Tateyuki Suzuki
Keyword(s):  
Mach Reflection ◽  
Von Neumann ◽  
Von Neumann Paradox ◽  
Self Similar

On the von Neumann paradox of weak Mach reflection

1989 ◽  
Vol 4 (5-6) ◽  
pp. 333-345 ◽  
Author(s):  
Akira Sakurai ◽  
L F Henderson ◽  
Kazuyoshi Takayama ◽  
Zbigniew Walenta ◽  
Philip Colella
Keyword(s):  
Mach Reflection ◽  
Von Neumann ◽  
Von Neumann Paradox
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