scholarly journals Nonlinear acoustics and shock formation in lossless barotropic Green--Naghdi fluids

2016 ◽  
Vol 5 (3) ◽  
pp. 349-365 ◽  
Author(s):  
Ivan C. Christov
Keyword(s):  
Nonlinear Acoustics ◽  
Shock Formation

NONLINEAR ACOUSTICS APPLICATIONS FOR NEAR WELLBORE FORMATION EVALUATION

2020 ◽  
Author(s):  
Christopher Skelt ◽  
◽  
James TenCate ◽  
Robert Guyer ◽  
Paul Johnson ◽  
...  
Keyword(s):  
Nonlinear Acoustics ◽  
Formation Evaluation

The time-asymptotic stability of shocks in cosmic-ray hydrodynamics

1988 ◽  
Vol 39 (3) ◽  
pp. 539-548 ◽  
Author(s):  
G. P. Zank
Keyword(s):  
Wave Equation ◽  
Asymptotic Stability ◽  
Short Wavelength ◽  
Cosmic Ray ◽  
Hydrodynamical Model ◽  
Shock Formation ◽  
Nonlinear Behaviour ◽  
Two Fluid

The nonlinear behaviour of short-wavelength perturbations in the two-fluid cosmic-ray hydrodynamical model is examined. We show that such a perturbation leads to shock formation and derive the appropriate wave equation. We show that a discontinuous perturbation incident on a weak cosmic-ray shock destabilizes, in a time-asymptotic sense, the shock.

Shock formation induced by poloidal flow and its effects on the edge stability in tokamaks

2016 ◽  
Vol 23 (4) ◽  
pp. 042501 ◽  
Author(s):  
J. Seol ◽  
K. C. Shaing ◽  
A. Y. Aydemir
Keyword(s):  
Shock Formation ◽  
Edge Stability

Transonic Shock Formation in a Rarefaction Riemann Problem for the 2D Compressible Euler Equations

2008 ◽  
Vol 69 (3) ◽  
pp. 720-742 ◽  
Author(s):  
James Glimm ◽  
Xiaomei Ji ◽  
Jiequan Li ◽  
Xiaolin Li ◽  
Peng Zhang ◽  
...  
Keyword(s):  
Euler Equations ◽  
Riemann Problem ◽  
Compressible Euler Equations ◽  
Shock Formation ◽  
Transonic Shock ◽  
Compressible Euler

FINITE ELEMENT METHODS FOR NONLINEAR ACOUSTICS IN FLUIDS

2007 ◽  
Vol 15 (03) ◽  
pp. 353-375 ◽  
Author(s):  
TIMOTHY WALSH ◽  
MONICA TORRES
Keyword(s):  
Finite Element ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Acoustics ◽  
Time Step ◽  
Partial Differential ◽  
Time Step Size ◽  
Finite Element Discretizations ◽  
Acoustic Fluid ◽  
Element Discretizations

In this paper, weak formulations and finite element discretizations of the governing partial differential equations of three-dimensional nonlinear acoustics in absorbing fluids are presented. The fluid equations are considered in an Eulerian framework, rather than a displacement framework, since in the latter case the corresponding finite element formulations suffer from spurious modes and numerical instabilities. When taken with the governing partial differential equations of a solid body and the continuity conditions, a coupled formulation is derived. The change in solid/fluid interface conditions when going from a linear acoustic fluid to a nonlinear acoustic fluid is demonstrated. Finite element discretizations of the coupled problem are then derived, and verification examples are presented that demonstrate the correctness of the implementations. We demonstrate that the time step size necessary to resolve the wave decreases as steepening occurs. Finally, simulation results are presented on a resonating acoustic cavity, and a coupled elastic/acoustic system consisting of a fluid-filled spherical tank.

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