A new approach to problems of shock dynamics Part I Two-dimensional problems

In this paper, two-dimensional problems of the diffraction and stability of shock waves are investigated using an approximate theory in which disturbances to the flow are treated as a wave propagation on the shocks. These waves carry changes in the slope and the Mach number of the shock. The equations governing the wave propagation are analogous in every way to the non-linear equations for plane waves in gas dynamics, and their solutions can be deduced by the same mathematical techniques. Since the propagation speed of the waves is found to be an increasing function of Mach number, waves carrying an increase in Mach number will eventually break and form what we may call a ‘shock’, corresponding to the breaking of a compression wave into a shock in the ordinary plane wave case. Such a ‘shock’ moving on the shock is called ashock-shock.The shock-shock is a discontinuity in Mach number and shock slope, and it must be fitted in to satisfy the appropriate relations between these are interpreted as the trace of cylindrical sound waves in the flow behind the shock. In particular a shock-shock is the trace of a genuine shock in the flow behind, and thus corresponds to Mach reflection.The general theory of the wave propagation is set out in § 2. The subsequent sections contain applications of the theory to specific problems, including the motion of a shock along a curved wall, diffraction by a wedge, stability of plane shocks and the instability of a converging cylindrical shock.

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Measurement of shear wave propagation speed by estimation of two-dimensional wavenumbers using phase of particle velocity

Japanese Journal of Applied Physics ◽

10.7567/jjap.57.07lf07 ◽

2018 ◽

Vol 57 (7S1) ◽

pp. 07LF07 ◽

Cited By ~ 1

Author(s):

Masato Minagawa ◽

Hideyuki Hasegawa ◽

Tadashi Yamaguchi ◽

Shin-ichi Yagi

Keyword(s):

Wave Propagation ◽

Shear Wave ◽

Particle Velocity ◽

Propagation Speed ◽

Two Dimensional ◽

Wave Propagation Speed

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Osher Flux with Entropy Fix for Two-Dimensional Euler Equations

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2014.m469 ◽

2016 ◽

Vol 8 (4) ◽

pp. 670-692 ◽

Cited By ~ 1

Author(s):

Huajun Zhu ◽

Xiaogang Deng ◽

Meiliang Mao ◽

Huayong Liu ◽

Guohua Tu

Keyword(s):

Mach Number ◽

Euler Equations ◽

Mach Reflection ◽

Finite Volume Methods ◽

Second Order ◽

Two Dimensional ◽

First Order ◽

Shock Stability ◽

Double Mach Reflection ◽

High Mach

AbstractWe compare in this paper the properties of Osher flux with O-variant and P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the two-dimensional Euler equations and propose an entropy fix technique to improve their robustness. We consider both first-order and second-order reconstructions. For inviscid hypersonic flow past a circular cylinder, we observe different problems for different schemes: A first-order Osher-O scheme on quadrangular grids yields a carbuncle shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach number cases. In addition, a second-order Osher scheme can also yield a carbuncle shock or be unstable. To improve the robustness of these schemes we propose an entropy fix technique, and then present numerical results to show the effectiveness of the proposed method. In addition, the influence of grid aspects ratio, relative shock position to the grid and Mach number on shock stability are tested. Viscous heating problem and double Mach reflection problem are simulated to test the influence of the entropy fix on contact resolution and boundary layer resolution.

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Decoupling of plane waves in porous piezoelectric materials

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2014.0172 ◽

2014 ◽

Vol 470 (2169) ◽

pp. 20140172

Author(s):

Anil K. Vashishth ◽

Vishakha Gupta

Keyword(s):

Wave Propagation ◽

Symmetry Group ◽

Piezoelectric Materials ◽

Pure Shear ◽

Plane Waves ◽

Two Dimensional ◽

Numerical Studies ◽

Piezoelectric Effects ◽

Crystal Class ◽

Dimensional Wave

In this paper, the analytical and numerical studies of two-dimensional wave propagation in porous piezoelectric materials (PPMs) are carried out. The decoupling of waves, in such materials for various crystal classes, is studied analytically for different coordinate planes. It is found that, for wave propagation in a plane, the system is decoupled in some crystal classes, whereas it remains coupled in other crystal classes. It is established that the decoupled pure-shear wave, propagating in a PPM, can be stiffened or unstiffened with piezoelectric effects even if the PPM belongs to the same symmetry group but has a different crystal class. The skewing angles and mutual angles between the polarization directions of different waves are also computed numerically.

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Acoustic wave propagation in two dimensional sheared ducted flows

10.2514/6.1997-1631 ◽

1997 ◽

Author(s):

E. Longatte ◽

P. Lafon ◽

S. Candel ◽

E. Longatte ◽

P. Lafon ◽

...

Keyword(s):

Wave Propagation ◽

Acoustic Wave ◽

Two Dimensional ◽

Acoustic Wave Propagation

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Influence of the applied pressure of the transducer on the propagation speed of the ultrasonic wave in wood

Holzforschung ◽

10.1515/hf-2020-0272 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Edgar V.M. Carrasco ◽

Rejane C. Alves ◽

Mônica A. Smits ◽

Vinnicius D. Pizzol ◽

Ana Lucia C. Oliveira ◽

...

Keyword(s):

Wave Propagation ◽

Applied Pressure ◽

Pressure Gauge ◽

Eucalyptus Grandis ◽

Propagation Speed ◽

Ultrasonic Waves ◽

Ultrasonic Speed ◽

Wave Propagation Speed ◽

Propagation Technique ◽

Non Destructive

Abstract The non-destructive wave propagation technique is used to estimate the wood’s modulus of elasticity. The propagation speed of ultrasonic waves is influenced by some factors, among them: the type of transducer used in the test, the form of coupling and the sensitivity of the transducers. The objective of the study was to evaluate the influence of the contact pressure of the transducers on the ultrasonic speed. Ninety-eight tests were carried out on specimens of the species Eucalyptus grandis, with dimensions of 120 × 120 × 50 mm. The calibration of the pressure exerted by the transducer was controlled by a pressure gauge using a previously calibrated load cell. The robust statistical analysis allowed to validate the experimental results and to obtain consistent conclusions. The results showed that the wave propagation speed is not influenced by the pressure exerted by the transducer.

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Study on X-ray Induced Two-Dimensional Thermal Shock Waves in Carbon/Phenolic

Materials ◽

10.3390/ma14133553 ◽

2021 ◽

Vol 14 (13) ◽

pp. 3553

Author(s):

Dengwang Wang ◽

Yong Gao ◽

Sheng Wang ◽

Jie Wang ◽

Haipeng Li

Keyword(s):

Numerical Simulation ◽

Shock Wave ◽

Wave Propagation ◽

Thermal Shock ◽

Anisotropic Material ◽

Energy Deposition ◽

X Rays ◽

Two Dimensional ◽

X Ray ◽

Deposition Depth

Carbon/Phenolic (C/P), a typical anisotropic material, is an important component of aerospace and often used to protect the thermodynamic effects of strong X-ray radiation. In this paper, we establish the anisotropic elastic-plastic constitutive model, which is embedded in the in-house code “RAMA” to simulate a two-dimensional thermal shock wave induced by X-ray. Then, we compare the numerical simulation results with the thermal shock wave stress generated by the same strong current electron beam via experiment to verify the correctness of the numerical simulation. Subsequently, we discuss and analyze the rules of thermal shock wave propagation in C/P material by further numerical simulation. The results reveal that the thermal shock wave represents different shapes and mechanisms by the radiation of 1 keV and 3 keV X-rays. The vaporization recoil phenomenon appears as a compression wave under 1 keV X-ray irradiation, and X-ray penetration is caused by thermal deformation under 3 keV X-ray irradiation. The thermal shock wave propagation exhibits two-dimensional characteristics, the energy deposition of 1 keV and 3 keV both decays exponentially, the energy deposition of 1 keV-peak soft X-ray is high, and the deposition depth is shallow, while the energy deposition of 3 keV-peak hard X-ray is low, and the deposition depth is deep. RAMA can successfully realize two-dimensional orthotropic elastoplastic constitutive relation, the corresponding program was designed and checked, and the calculation results for inspection are consistent with the theory. This study has great significance in the evaluation of anisotropic material protection under the radiation of intense X-rays.

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Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

Zeitschrift für Naturforschung A ◽

10.1515/zna-1990-11-1201 ◽

1990 ◽

Vol 45 (11-12) ◽

pp. 1219-1229 ◽

Cited By ~ 1

Author(s):

D.-A. Becker ◽

E. W. Richter

Keyword(s):

Differential Equations ◽

Linear Equations ◽

Mhd Equations ◽

Two Dimensional ◽

Invariant Solutions ◽

First Order ◽

Partially Invariant Solutions ◽

Quasilinear Systems ◽

Ideal Mhd ◽

Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

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Reducing a Class of Two-Dimensional Integrals to One-Dimension with an Application to Gaussian Transforms

Atoms ◽

10.3390/atoms8030053 ◽

2020 ◽

Vol 8 (3) ◽

pp. 53

Author(s):

Jack C. Straton

Keyword(s):

Quantum Theory ◽

Arbitrary Function ◽

Plane Waves ◽

Wave Functions ◽

One Dimension ◽

Two Dimensional ◽

Transition Amplitudes ◽

Multidimensional Integrals ◽

Coulomb Potentials

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers multiplied by an arbitrary function of xy/(x+y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.

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