Skip to main content
Top

2020 | OriginalPaper | Chapter

7. Solutions of Computational Acoustic Problems Using DRP Schemes

Authors : Tapan K. Sengupta, Yogesh G. Bhumkar

Published in: Computational Aerodynamics and Aeroacoustics

Publisher: Springer Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Computational acoustics is an important and active research area [12, 13, 45, 47, 49]. Acoustic signals propagate in the form of longitudinal waves in air. Pressure fluctuations associated with acoustic signals are usually very small compared to the large background pressure field. The atmospheric pressure is around \(10^{5}\) Pa, while the amplitude of the smallest recognizable acoustic disturbance for a human being is around \(10^{-5}\) Pa.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference G. Ashcroft, X. Zhang, Optimized prefactored compact schemes. J. Comput. Phys. 190(2), 459–477 (2003)MATHCrossRef G. Ashcroft, X. Zhang, Optimized prefactored compact schemes. J. Comput. Phys. 190(2), 459–477 (2003)MATHCrossRef
2.
go back to reference C. Bailly, D. Juve, Numerical solution of acoustic propagation problems using linearized euler equations. AIAA J. 38(1), 22–29 (2000)CrossRef C. Bailly, D. Juve, Numerical solution of acoustic propagation problems using linearized euler equations. AIAA J. 38(1), 22–29 (2000)CrossRef
3.
go back to reference M. Bernardini, S. Pirozzoli, A general strategy for the optimization of runge-kutta schemes for wave propagation phenomena. J. Comput. Phys. 228(11), 4182–4199 (2009)MATHCrossRef M. Bernardini, S. Pirozzoli, A general strategy for the optimization of runge-kutta schemes for wave propagation phenomena. J. Comput. Phys. 228(11), 4182–4199 (2009)MATHCrossRef
4.
go back to reference Y.G. Bhumkar, High Performance Computing of Bypass Transition. Ph.D. Thesis, Department of Aerospace Engineering, Indian Institute of Technology, Kanpur (2012) Y.G. Bhumkar, High Performance Computing of Bypass Transition. Ph.D. Thesis, Department of Aerospace Engineering, Indian Institute of Technology, Kanpur (2012)
5.
go back to reference Y.G. Bhumkar, T.K. Sengupta, Adaptive multi-dimensional filters. Comput. Fluids 49 (2011) Y.G. Bhumkar, T.K. Sengupta, Adaptive multi-dimensional filters. Comput. Fluids 49 (2011)
6.
go back to reference Y.G. Bhumkar, T.W.H. Sheu, T.K. Sengupta, A dispersion relation preserving optimized upwind compact difference scheme for high accuracy flow simulations. J. Comput. Phys. 278, 378–399 (2014)MathSciNetMATHCrossRef Y.G. Bhumkar, T.W.H. Sheu, T.K. Sengupta, A dispersion relation preserving optimized upwind compact difference scheme for high accuracy flow simulations. J. Comput. Phys. 278, 378–399 (2014)MathSciNetMATHCrossRef
7.
go back to reference B.J. Boersma, A staggered compact finite difference formulation for the compressible Navier-Stokes equations. J. Comput. Phys. 208(2), 675–690 (2005)MATHCrossRef B.J. Boersma, A staggered compact finite difference formulation for the compressible Navier-Stokes equations. J. Comput. Phys. 208(2), 675–690 (2005)MATHCrossRef
8.
go back to reference C. Bogey, C. Bailly, D. Juv\(\acute{e}\), Noise investigation of a high subsonic, moderate reynolds number jet using a compressible LES. Theor. Comput. Fluid Dyn. 16(4), 273–297 (2003) C. Bogey, C. Bailly, D. Juv\(\acute{e}\), Noise investigation of a high subsonic, moderate reynolds number jet using a compressible LES. Theor. Comput. Fluid Dyn. 16(4), 273–297 (2003)
9.
go back to reference V. Borue, S.A. Orszag, Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31 (1998)MathSciNetMATHCrossRef V. Borue, S.A. Orszag, Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31 (1998)MathSciNetMATHCrossRef
10.
go back to reference P.H. Chiu, T.W.H. Sheu, On the development of a dispersion-relation-preserving dual-compact upwind scheme for convection-diffusion equation. J. Comput. Phys. 228, 3640–3655 (2009) P.H. Chiu, T.W.H. Sheu, On the development of a dispersion-relation-preserving dual-compact upwind scheme for convection-diffusion equation. J. Comput. Phys. 228, 3640–3655 (2009)
12.
go back to reference T. Colonius, S.K. Lele, Computational aeroacoustics: progress on nonlinear problems of sound generation. Prog. Aero. Sci. 40, 345–416 (2004)CrossRef T. Colonius, S.K. Lele, Computational aeroacoustics: progress on nonlinear problems of sound generation. Prog. Aero. Sci. 40, 345–416 (2004)CrossRef
13.
go back to reference H.A.V. der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 13, 631–644 (1992)MATHCrossRef H.A.V. der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 13, 631–644 (1992)MATHCrossRef
14.
go back to reference K.Y. Fung, R.S.O. Man, S. Davis, A compact solution to computational acoustics, in ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA) (1995), pp. 59–72 K.Y. Fung, R.S.O. Man, S. Davis, A compact solution to computational acoustics, in ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA) (1995), pp. 59–72
15.
go back to reference D.V. Gaitonde, J.S. Shang, J.L. Young, Practical aspects of higher-order numerical schemes for wave propagation phenomena. Int. J. Numer. Meth. Eng. 45(12), 1849–1869 (1999)MATHCrossRef D.V. Gaitonde, J.S. Shang, J.L. Young, Practical aspects of higher-order numerical schemes for wave propagation phenomena. Int. J. Numer. Meth. Eng. 45(12), 1849–1869 (1999)MATHCrossRef
16.
go back to reference S.I. Green, Fluid Vortices: Fluid Mechanics and Its Applications (Springer, Berlin, 1995) S.I. Green, Fluid Vortices: Fluid Mechanics and Its Applications (Springer, Berlin, 1995)
17.
go back to reference N. Haugen, A. Brandenburg, Inertial range scaling in numerical turbulence with hyperviscosity. Phys. Rev. E 70, 026405 (2004) N. Haugen, A. Brandenburg, Inertial range scaling in numerical turbulence with hyperviscosity. Phys. Rev. E 70, 026405 (2004)
18.
go back to reference A.E. Honein, P. Moin, Higher entropy conservation and numerical stability of compressible turbulence simulations. J. Comput. Phys. 201(2), 531–545 (2004)MATHCrossRef A.E. Honein, P. Moin, Higher entropy conservation and numerical stability of compressible turbulence simulations. J. Comput. Phys. 201(2), 531–545 (2004)MATHCrossRef
19.
go back to reference G.S. Karamanos, G.E. Karniadakis, A spectral vanishing viscosity method for large-eddy simulations. J. Comput. Phys. 163(1), 22–50 (2000)MathSciNetMATHCrossRef G.S. Karamanos, G.E. Karniadakis, A spectral vanishing viscosity method for large-eddy simulations. J. Comput. Phys. 163(1), 22–50 (2000)MathSciNetMATHCrossRef
20.
go back to reference T. Kawai, Sound diffraction by a many-sided barrier or pillar. J. Sound Vib. 79(2), 229–242 (1981)MATHCrossRef T. Kawai, Sound diffraction by a many-sided barrier or pillar. J. Sound Vib. 79(2), 229–242 (1981)MATHCrossRef
21.
go back to reference L.E. Kinsler, A.R. Frey, A.B. Coppens, J.V. Sanders, Fundamentals of Acoustics (Wiley, New York, 2000) L.E. Kinsler, A.R. Frey, A.B. Coppens, J.V. Sanders, Fundamentals of Acoustics (Wiley, New York, 2000)
22.
go back to reference E. Lamballais, V. Fortun\(\acute{e}\), S.L. Aizet, Straightforward high-order numerical dissipation via the viscous term for direct and large eddy simulation. J. Comput. Phys. 230(9), 3270–3275 (2011) E. Lamballais, V. Fortun\(\acute{e}\), S.L. Aizet, Straightforward high-order numerical dissipation via the viscous term for direct and large eddy simulation. J. Comput. Phys. 230(9), 3270–3275 (2011)
23.
go back to reference A.G. Lamorgese, D.A. Caughey, S.B. Pope, Direct numerical simulation of homogeneous turbulence with hyperviscosity. Phys. Fluids 17 (2005) A.G. Lamorgese, D.A. Caughey, S.B. Pope, Direct numerical simulation of homogeneous turbulence with hyperviscosity. Phys. Fluids 17 (2005)
25.
go back to reference M.J. Lighthill, On sound generated aerodynamically. I. general theory. Proc. Roy. Soc. Lond. A: Math. Phys. Eng. Sci. 211, 564–587 (1952) M.J. Lighthill, On sound generated aerodynamically. I. general theory. Proc. Roy. Soc. Lond. A: Math. Phys. Eng. Sci. 211, 564–587 (1952)
26.
27.
go back to reference S. Nagarajan, S.K. Lele, J.H. Ferziger, A robust high-order compact method for large eddy simulation. J. Comput. Phys. 191(2), 392–419 (2003)MathSciNetMATHCrossRef S. Nagarajan, S.K. Lele, J.H. Ferziger, A robust high-order compact method for large eddy simulation. J. Comput. Phys. 191(2), 392–419 (2003)MathSciNetMATHCrossRef
28.
go back to reference R. Pasquetti, Spectral vanishing viscosity method for large-eddy simulation of turbulent flows. J. Sci. Comput. 27, 365–375 (2006)MathSciNetMATHCrossRef R. Pasquetti, Spectral vanishing viscosity method for large-eddy simulation of turbulent flows. J. Sci. Comput. 27, 365–375 (2006)MathSciNetMATHCrossRef
29.
go back to reference S. Pirozzoli, Performance analysis and optimization of finite-difference schemes for wave propagation problems. J. Comput. Phys. 222(2), 809–831 (2007)MathSciNetMATHCrossRef S. Pirozzoli, Performance analysis and optimization of finite-difference schemes for wave propagation problems. J. Comput. Phys. 222(2), 809–831 (2007)MathSciNetMATHCrossRef
30.
go back to reference T. Poinsot, D. Veynante, Theoretical and Numerical Combustion. R. T. Edwards Inc., (2005) T. Poinsot, D. Veynante, Theoretical and Numerical Combustion. R. T. Edwards Inc., (2005)
31.
go back to reference J. Pradhan, S. Jindal, B. Mahato, Y.G. Bhumkar, Joint optimization of the spatial and the temporal discretization scheme for accurate computation of acoustic problems. Commun. Comput. Phys. 24(2), 408–434 (2018) J. Pradhan, S. Jindal, B. Mahato, Y.G. Bhumkar, Joint optimization of the spatial and the temporal discretization scheme for accurate computation of acoustic problems. Commun. Comput. Phys. 24(2), 408–434 (2018)
32.
go back to reference J. Pradhan, B. Mahato, S.D. Dhandole, Y.G. Bhumkar, Construction, analysis and application of coupled compact difference scheme in computational acoustics and fluid flow problems. Commun. Comput. Phys. 18(4), 957–984 (2015)MathSciNetMATHCrossRef J. Pradhan, B. Mahato, S.D. Dhandole, Y.G. Bhumkar, Construction, analysis and application of coupled compact difference scheme in computational acoustics and fluid flow problems. Commun. Comput. Phys. 18(4), 957–984 (2015)MathSciNetMATHCrossRef
33.
go back to reference M.K. Rajpoot, T.K. Sengupta, P.K. Dutt, Optimal time advancing dispersion relation preserving schemes. J. Comput. Phys. 229, 3623–3651 (2010)MathSciNetMATHCrossRef M.K. Rajpoot, T.K. Sengupta, P.K. Dutt, Optimal time advancing dispersion relation preserving schemes. J. Comput. Phys. 229, 3623–3651 (2010)MathSciNetMATHCrossRef
34.
go back to reference T. Rylander, P. Ingelström, A. Bondeson, Computational Electromagnetics (Springer, Berlin, 2007) T. Rylander, P. Ingelström, A. Bondeson, Computational Electromagnetics (Springer, Berlin, 2007)
35.
go back to reference N.D. Sandham, Q. Li, H.C. Yee, Entropy splitting for high-order numerical simulation of compressible turbulence. J. Comput. Phys. 178(2), 307–322 (2002)MATHCrossRef N.D. Sandham, Q. Li, H.C. Yee, Entropy splitting for high-order numerical simulation of compressible turbulence. J. Comput. Phys. 178(2), 307–322 (2002)MATHCrossRef
36.
go back to reference T.K. Sengupta, S. Bhaumik, Y.G. Bhumkar, Direct numerical simulation of two-dimensional wall-bounded turbulent flows from receptivity stage. Phys. Rev. E 85(2), 026308 (2012) T.K. Sengupta, S. Bhaumik, Y.G. Bhumkar, Direct numerical simulation of two-dimensional wall-bounded turbulent flows from receptivity stage. Phys. Rev. E 85(2), 026308 (2012)
37.
go back to reference T.K. Sengupta, High Accuracy Computing Methods: Fluid Flows and Wave Phenomena (Cambridge University Press, USA, 2013)MATHCrossRef T.K. Sengupta, High Accuracy Computing Methods: Fluid Flows and Wave Phenomena (Cambridge University Press, USA, 2013)MATHCrossRef
38.
go back to reference T.K. Sengupta, Y.G. Bhumkar, New explicit two-dimensional higher order filters. Comput. Fluids 39, 1848–1863 (2010)MATHCrossRef T.K. Sengupta, Y.G. Bhumkar, New explicit two-dimensional higher order filters. Comput. Fluids 39, 1848–1863 (2010)MATHCrossRef
39.
go back to reference T.K. Sengupta, G. Ganeriwal, S. De, Analysis of central and upwind compact schemes. J. Comput. Phys. 192, 677–694 (2003)MATHCrossRef T.K. Sengupta, G. Ganeriwal, S. De, Analysis of central and upwind compact schemes. J. Comput. Phys. 192, 677–694 (2003)MATHCrossRef
40.
41.
42.
go back to reference T.K. Sengupta, Y.G. Bhumkar, V. Lakshmanan, Design and analysis of a new filter for LES and DES. Comput. Struct. 87, 735–750 (2009)CrossRef T.K. Sengupta, Y.G. Bhumkar, V. Lakshmanan, Design and analysis of a new filter for LES and DES. Comput. Struct. 87, 735–750 (2009)CrossRef
43.
go back to reference T.K. Sengupta, V. Lakshmanan, V.V.S.N. Vijay, A new combined stable and dispersion relation preserving compact scheme for non-periodic problems. J. Comput. Phys. 228, 3048–3071 (2009)MathSciNetMATHCrossRef T.K. Sengupta, V. Lakshmanan, V.V.S.N. Vijay, A new combined stable and dispersion relation preserving compact scheme for non-periodic problems. J. Comput. Phys. 228, 3048–3071 (2009)MathSciNetMATHCrossRef
44.
go back to reference T.K. Sengupta, V.V.S.N. Vijay, S. Bhaumik, Further improvement and analysis of CCD scheme: dissipation discretization and de-aliasing properties. J. Comput. Phys. 228(17), 6150–6168 (2009)MATHCrossRef T.K. Sengupta, V.V.S.N. Vijay, S. Bhaumik, Further improvement and analysis of CCD scheme: dissipation discretization and de-aliasing properties. J. Comput. Phys. 228(17), 6150–6168 (2009)MATHCrossRef
45.
go back to reference T.K. Sengupta, M.K. Rajpoot, S. Saurabh, V.V.S.N. Vijay, Analysis of anisotropy of numerical wave solutions by high accuracy finite difference methods. J. Comput. Phys. 230, 27–60 (2011)MathSciNetMATHCrossRef T.K. Sengupta, M.K. Rajpoot, S. Saurabh, V.V.S.N. Vijay, Analysis of anisotropy of numerical wave solutions by high accuracy finite difference methods. J. Comput. Phys. 230, 27–60 (2011)MathSciNetMATHCrossRef
46.
go back to reference T.K. Sengupta, Y.G. Bhumkar, M. Rajpoot, V.K. Suman, S. Saurabh, Spurious waves in discrete computation of wave phenomena and flow problems. Appl. Math. Comput. 218, 9035–9065 (2012)MathSciNetMATH T.K. Sengupta, Y.G. Bhumkar, M. Rajpoot, V.K. Suman, S. Saurabh, Spurious waves in discrete computation of wave phenomena and flow problems. Appl. Math. Comput. 218, 9035–9065 (2012)MathSciNetMATH
47.
go back to reference T.K. Sengupta, Y.G. Bhumkar, S. Sengupta, Dynamics and instability of a shielded vortex in close proximity of a wall. Comput. Fluids 70, 166–175 (2012)MathSciNetMATHCrossRef T.K. Sengupta, Y.G. Bhumkar, S. Sengupta, Dynamics and instability of a shielded vortex in close proximity of a wall. Comput. Fluids 70, 166–175 (2012)MathSciNetMATHCrossRef
48.
go back to reference P.L. Shah, J. Hardin, Second-order numerical solution of time-dependent, first-order hyperbolic equations, in ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA) (1995), pp. 133–141 P.L. Shah, J. Hardin, Second-order numerical solution of time-dependent, first-order hyperbolic equations, in ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA) (1995), pp. 133–141
49.
50.
go back to reference C.K.W. Tam, J.C. Hardin, Second computational aeroacoustics (caa) workshop on benchmark problems, in NASA Conference Publication (1997), p. 3352 C.K.W. Tam, J.C. Hardin, Second computational aeroacoustics (caa) workshop on benchmark problems, in NASA Conference Publication (1997), p. 3352
51.
go back to reference C.K.W. Tam, K.A. Kurbatskii, J. Fang, Numerical boundary conditions for computational aeroacoustics benchmark problems, in NASA Conference Publication (1997), p. 3352 C.K.W. Tam, K.A. Kurbatskii, J. Fang, Numerical boundary conditions for computational aeroacoustics benchmark problems, in NASA Conference Publication (1997), p. 3352
52.
go back to reference C.K.W. Tam, H. Shen, K.A. Kurbatskii, L. Auriault, Z. Dong, J.C. Webb, Solutions of the benchmark problems by the dispersion-relation-preserving scheme, in ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA), vol. 1 (1995), pp. 149–172 C.K.W. Tam, H. Shen, K.A. Kurbatskii, L. Auriault, Z. Dong, J.C. Webb, Solutions of the benchmark problems by the dispersion-relation-preserving scheme, in ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA), vol. 1 (1995), pp. 149–172
53.
go back to reference C.K.W. Tam, Computational Aeroacoustics a Wave Number Approach (Cambridge University Press, New York, 2012)MATHCrossRef C.K.W. Tam, Computational Aeroacoustics a Wave Number Approach (Cambridge University Press, New York, 2012)MATHCrossRef
54.
go back to reference C.K.W. Tam, Z. Dong, Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow. J. Comput. Acoust. 4(2), 175–201 (1996)CrossRef C.K.W. Tam, Z. Dong, Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow. J. Comput. Acoust. 4(2), 175–201 (1996)CrossRef
55.
go back to reference C.K.W. Tam, J.C. Webb, Dispersion-relation-preserving finite difference schemes for computational acoustics. J. Comput. Phys. 107, 262–281 (1993)MathSciNetMATHCrossRef C.K.W. Tam, J.C. Webb, Dispersion-relation-preserving finite difference schemes for computational acoustics. J. Comput. Phys. 107, 262–281 (1993)MathSciNetMATHCrossRef
56.
go back to reference R. Vichnevetsky, J.B. Bowles, Fourier Analysis of Numerical Approximations of Hyperbolic Equations (SIAM Stud. Appl. Math, Philadelphia, 1982)MATHCrossRef R. Vichnevetsky, J.B. Bowles, Fourier Analysis of Numerical Approximations of Hyperbolic Equations (SIAM Stud. Appl. Math, Philadelphia, 1982)MATHCrossRef
57.
go back to reference M.R. Visbal, D.V. Gaitonde, On the use of higher-order finite-difference schemes on curvilinear and deforming meshes. J. Comput. Phys. 181, 155–185 (2002)MathSciNetMATHCrossRef M.R. Visbal, D.V. Gaitonde, On the use of higher-order finite-difference schemes on curvilinear and deforming meshes. J. Comput. Phys. 181, 155–185 (2002)MathSciNetMATHCrossRef
58.
go back to reference C.H. Yu, Y.G. Bhumkar, T.W.H. Sheu, Dispersion relation preserving combined compact difference schemes for flow problems. J. Sci. Comput. 62(2), 482–516 (2015)MathSciNetMATHCrossRef C.H. Yu, Y.G. Bhumkar, T.W.H. Sheu, Dispersion relation preserving combined compact difference schemes for flow problems. J. Sci. Comput. 62(2), 482–516 (2015)MathSciNetMATHCrossRef
59.
go back to reference Q. Zhou, Z. Yao, F. He, M.Y. Shen, A new family of high-order compact upwind difference schemes with good spectral resolution. J. Comput. Phys. 227, 1306–1339 (2007)MathSciNetMATHCrossRef Q. Zhou, Z. Yao, F. He, M.Y. Shen, A new family of high-order compact upwind difference schemes with good spectral resolution. J. Comput. Phys. 227, 1306–1339 (2007)MathSciNetMATHCrossRef
Metadata
Title
Solutions of Computational Acoustic Problems Using DRP Schemes
Authors
Tapan K. Sengupta
Yogesh G. Bhumkar
Copyright Year
2020
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-15-4284-8_7

Premium Partners