Numerical Solution of Acoustic Propagation Problems Using Linearized Euler Equations

AIAA Journal ◽  
10.2514/2.949 ◽  
2000 ◽  
Vol 38 (1) ◽  
pp. 22-29 ◽  
Author(s):  
Christophe Bailly ◽  
Daniel Juvé
Keyword(s):  
Numerical Solution ◽  
Euler Equations ◽  
Acoustic Propagation ◽  
Linearized Euler Equations

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.

Numerical Solution of the Linearized Euler Equations Using Compact Schemes

2009 ◽  
pp. 837-842
Author(s):  
Kris Van den Abeele ◽  
Jan Ramboer ◽  
Ghader Ghorbaniasl ◽  
Chris Lacor
Keyword(s):  
Numerical Solution ◽  
Euler Equations ◽  
Compact Schemes ◽  
Linearized Euler Equations

Broadband liner impedance eduction for multimodal acoustic propagation in the presence of a mean flow

2016 ◽  
Vol 11 (2) ◽  
pp. 150-155
Author(s):  
R. Troian ◽  
D. Dragna ◽  
C. Bailly ◽  
M.-A. Galland
Keyword(s):  
Numerical Model ◽  
Flow Characteristics ◽  
Acoustic Propagation ◽  
Rational Fraction ◽  
Physical Parameters ◽  
Mean Flow ◽  
Linearized Euler Equations ◽  
Grazing Flow ◽  
Propagation Medium ◽  
Difference Time

Modeling of acoustic propagation in a duct with absorbing treatment is considered. The surface impedance of the treatment is sought in the form of a rational fraction. The numerical model is based on a resolution of the linearized Euler equations by finite difference time domain for the calculation of the acoustic propagation under a grazing flow. Sensitivity analysis of the considered numerical model is performed. The uncertainty of the physical parameters is taken into account to determine the most influential input parameters. The robustness of the solution vis-a-vis changes of the flow characteristics and the propagation medium is studied.

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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