Evaluating a linearized Euler equations model for strong turbulence effects on sound propagation

2013 ◽  
Vol 133 (4) ◽  
pp. 1922-1933 ◽  
Author(s):  
Loïc Ehrhardt ◽  
Sylvain Cheinet ◽  
Daniel Juvé ◽  
Philippe Blanc-Benon
Keyword(s):  
Euler Equations ◽  
Sound Propagation ◽  
Linearized Euler Equations ◽  
Strong Turbulence ◽  
Turbulence Effects

SPECTRAL ELEMENT METHOD FOR ACOUSTIC PROPAGATION PROBLEMS BASED ON LINEARIZED EULER EQUATIONS

2009 ◽  
Vol 17 (04) ◽  
pp. 383-402 ◽  
Author(s):  
RONGXIN ZHANG ◽  
GUOLIANG QIN ◽  
CHANGYUN ZHU
Keyword(s):  
Euler Equations ◽  
Sound Propagation ◽  
Spectral Element ◽  
Acoustic Propagation ◽  
Absorbing Boundary Conditions ◽  
Element Approximation ◽  
Newmark Method ◽  
Mean Flow ◽  
Linearized Euler Equations ◽  
Accuracy And Stability

A Chebyshev spectral element approximation of acoustic propagation problems based on linearized Euler equations is introduced, and the numerical approach is based on spectral elements in space with first-order Clayton–Engquist–Majda absorbing boundary conditions and implicit Newmark method in time. An initial perturbation problem has been solved to test the accuracy and stability of the numerical method. Then the sound propagation by source terms is also studied, including the radiation of a monopole and dipolar source in both stationary medium and uniform mean flow. The numerical simulation leads to good results in both accuracy and stability. Compared with the analytical solutions, the numerical results show the advantages in spectral accuracy even with relatively fewer grid points. Moreover, the implicit Newmark method in time marching also presents its superiority in stability. Finally, a problem of sound propagation in pipes is simulated as well.

scholarly journals The Concepts of Well-Posedness and Stability in Different Function Spaces for the 1D Linearized Euler Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Stefan Balint ◽  
Agneta M. Balint
Keyword(s):  
Euler Equation ◽  
Function Space ◽  
Euler Equations ◽  
Small Perturbation ◽  
Function Spaces ◽  
Well Posedness ◽  
Small Solution ◽  
Null Solution ◽  
Linearized Euler Equations ◽  
The Stability

This paper considers the stability of constant solutions to the 1D Euler equation. The idea is to investigate the effect of different function spaces on the well-posedness and stability of the null solution of the 1D linearized Euler equations. It is shown that the mathematical tools and results depend on the meaning of the concepts “perturbation,” “small perturbation,” “solution of the propagation problem,” and “small solution, that is, solution close to zero,” which are specific for each function space.

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