The partition of unity finite element method for short wave acoustic propagation on non-uniform potential flows

International Journal for Numerical Methods in Engineering

Volumn 65, Issue 3, 2006, Pages 425-444

  Gamallo, P ^a   Astley, R J ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Partition of unity method; Potential flow acoustics; Short wave problems

Indexed keywords

ACOUSTIC WAVE PROPAGATION; APPROXIMATION THEORY; COMPUTATIONAL FLUID DYNAMICS; ERROR ANALYSIS; MATHEMATICAL MODELS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

PARTITION OF UNITY METHOD; POTENTIAL FLOW ACOUSTICS; SHORT WAVE ACOUSTIC PROPAGATION; SHORT WAVE PROBLEMS;

FINITE ELEMENT METHOD;

MATHEMATICAL ANALYSIS;

EID: 30644469853     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1459     Document Type: Article

References (20)

1. Eversman W. Mapped infinite wave envelope elements for acoustic radiation in a uniformly moving medium. Journal of Sound and Vibration 1999; 224:665-687.
2. Astley RJ, Hamilton JA, Baker N, Kitchen E. Modelling tone propagation from turbofan inlets - the effect of extended lip liners. AIAA Paper 2002; No. 2002-2449.
3. Stanescu D, Xu J, Hussaini MY, Farassat F. Computation of engine noise propagation and scattering off an aircraft. International Journal of Aeroacoustics 2002; 1:403-420.
4. Deraemaeker A, Babuska I, Bouillard P. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. International Journal for Numerical Methods in Engineering 1999; 46:471-499.
5. Melenk JM, Babuška I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139:289-314.
6. Laghrouche O, Bettess P. Short wave modelling using special finite elements. Journal of Computational Acoustics 2000; 8(1):189-210.
7. Laghrouche O, Bettess P, Astley RJ. Modelling of short wave diffraction problems using approximating systems of plane waves. International Journal for Numerical Methods in Engineering 2002; 54:1501-1533.
8. Myers MK. On the acoustic boundary condition in the presence of flow. Journal of Sound and Vibration 1980; 71:429-434.
9. Eversman W. The boundary condition at an impedance wall in a non-uniform duct with potential mean flow. Journal of Sound and Vibration 2001; 246:63-69.
10. Eversman W. Errata. The boundary condition at an impedance wall in a non-uniform duct with potential mean flow. Journal of Sound and Vibration 2002; 258:791-792.
11. Ortiz P, Sanchez E. An improved partition of unity finite element model for diffraction problems. International Journal for Numerical Methods in Engineering 2001; 50:2727-2740.
12. Laghrouche O, Bettess P, Perrey-Debain E, Trevelyan J. Plane wave basis for wave scattering in three dimensions. Communications in Numerical Methods in Engineering 2003; 19:715-723.
13. Huttunen T, Gamallo P, Astley RJ. Comparison of two wave element methods for the Helmholtz problem. Computer Methods in Applied Mechanics and Engineering, submitted.
14. Tisseur F, Meerbergen K. The quadratic eigenvalue problem. SIAM Review 2001; 43(2):235-286.
15. Farhat C, Harari I, Franca LP. The discontinuous enrichment method. Computer Methods in Applied Mechanics and Engineering 2001; 190:6455-6479.
16. Bettess P, Shirron J, Laghrouche O, Peseux B, Sugimoto R, Trevelyan JA. A numerical integration scheme for special finite elements for the Helmholtz equation. International Journal for Numerical Methods in Engineering 2003; 56:531-552.
17. Astley RJ, Gamallo P. Special short wave elements for flow acoustics. Computer Methods in Applied Mechanics and Engineering 2005; 194:341-353.
18. Atkins HL. Continued development of the discontinuous Galerkin method for computational aeroacoustic applications. AIAA Paper 1997; No. 97-1581.
19. Eversman W. Theoretical models for duct acoustic propagation and radiation. Aeroacoustics of Flight Vehicles: Theory and Practice, WRDC Technical Report 90-3052. Noise control Nasa publication 1258, 1990.
20. Rienstra SW, Eversman W. A numerical comparison between the multiple scales and finite element solution for sound propagation in lined flow ducts. Journal of Fluid Mechanics 2001; 473:367-384.