Comptes Rendus
Strictly stable high order difference approximations for computational aeroacoustics
Comptes Rendus. Mécanique, Volume 333 (2005) no. 9, pp. 699-705.

High order finite difference approximations with improved accuracy and stability properties have been developed for computational aeroacoustics (CAA). One of our new difference operators corresponds to Tam and Webb's DRP scheme in the interior, but is modified near the boundaries to be strictly stable. A unified formulation of the nonlinear and linearized Euler equations is used, which can be extended to the Navier–Stokes equations. The approach has been verified for 1D, 2D and axisymmetric test problems. We have simulated the sound propagation from a rocket launch before lift-off.

Des schémas d'approximation par différences finies d'ordre élevé ont été développés pour l'aéroacoustique numérique dans le but d'accroître la précision et la stabilité. L'une de nos méthodes correspond au schéma de Tam et Webb, à l'intérieur du domaine, avec une modification aux limites du domaine qui permet d'obtenir une stabilité rigoureuse. Notre approche repose sur l'unification des équations non linéaires d'Euler et de leur forme linéarisée. Cette même approche pourrait être appliquée aux équations de Navier–Stokes. A titre d'exemple, la méthode est appliquée ici à des problèmes à une et deux dimensions, ainsi qu'à un problème axisymétrique. Un exemple simule l'acoustique induite par une fusée avant décollage.

Published online:
DOI: 10.1016/j.crme.2005.07.009
Keywords: Acoustics, Finite difference methods, High order, Aeroacoustics
Mot clés : Acoustique, Méthodes de différences finies, D'ordre élevée, Aéroacoustique

Bernhard Müller 1; Stefan Johansson 1

1 Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, 751 05 Uppsala, Sweden
@article{CRMECA_2005__333_9_699_0,
     author = {Bernhard M\"uller and Stefan Johansson},
     title = {Strictly stable high order difference approximations for computational aeroacoustics},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {699--705},
     publisher = {Elsevier},
     volume = {333},
     number = {9},
     year = {2005},
     doi = {10.1016/j.crme.2005.07.009},
     language = {en},
}
TY  - JOUR
AU  - Bernhard Müller
AU  - Stefan Johansson
TI  - Strictly stable high order difference approximations for computational aeroacoustics
JO  - Comptes Rendus. Mécanique
PY  - 2005
SP  - 699
EP  - 705
VL  - 333
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crme.2005.07.009
LA  - en
ID  - CRMECA_2005__333_9_699_0
ER  - 
%0 Journal Article
%A Bernhard Müller
%A Stefan Johansson
%T Strictly stable high order difference approximations for computational aeroacoustics
%J Comptes Rendus. Mécanique
%D 2005
%P 699-705
%V 333
%N 9
%I Elsevier
%R 10.1016/j.crme.2005.07.009
%G en
%F CRMECA_2005__333_9_699_0
Bernhard Müller; Stefan Johansson. Strictly stable high order difference approximations for computational aeroacoustics. Comptes Rendus. Mécanique, Volume 333 (2005) no. 9, pp. 699-705. doi : 10.1016/j.crme.2005.07.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.07.009/

[1] B. Gustafsson; H.-O. Kreiss; J. Oliger Time Dependent Problems and Difference Methods, John Wiley & Sons, New York, 1995

[2] B. Strand Summation by parts for finite difference approximations for d/dx, J. Comput. Phys., Volume 110 (1994), pp. 47-67

[3] B. Strand Simulations of acoustic wave phenomena using high-order finite difference approximations, SIAM J. Sci. Comput., Volume 20 (1999), pp. 1585-1604

[4] M. Gerritsen; P. Olsson Designing an efficient solution strategy for fluid flows, J. Comput. Phys., Volume 129 (1996), pp. 245-262

[5] J. Nordström; M.H. Carpenter Boundary and interface conditions for high-order finite-difference methods applied to the Euler and Navier–Stokes equations, J. Comput. Phys., Volume 148 (1999), pp. 621-645

[6] S. Johansson, High order finite difference operators with the summation by parts property based on DRP schemes, Technical Report 2004-036, Department of Information Technology, Uppsala University, 2004. URL: http://www.it.uu.se/research/reports/2004-036/

[7] C.K.W. Tam; J.C. Webb Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys., Volume 107 (1993), pp. 262-281

[8] H.C. Yee; M. Vinokur; M.J. Djomehri Entropy splitting and numerical dissipation, J. Comput. Phys., Volume 162 (2000), pp. 33-81

[9] B. Müller; H.C. Yee High order numerical simulation of sound generation by the Kirchhoff vortex, Computing and Visualization in Science, Volume 4 (2002), pp. 197-204

[10] B. Müller, High order difference method for low Mach number aeroacoustics, in: ECCOMAS Computational Fluid Dynamics Conference, Swansea, Wales, UK, 2001

[11] B. Müller; H.C. Yee Entropy splitting for high order numerical simulation of vortex sound at low Mach numbers, J. Sci. Comput., Volume 17 (2002) no. 1–4, pp. 181-190

[12] B. Müller, S. Johansson, Strictly stable high order difference approximations for the Euler equations, in: Proceedings of 10th Int. Congress on Sound and Vibration, Stockholm, 2003, pp. 3883–3890

[13] H.-O. Kreiss; G. Scherer Finite element and finite difference methods for hyperbolic partial differential equations (C. de Boor, ed.), Mathematical Aspects of Finite Elements in Partial Differential Equations, Academic Press, New York, 1974, pp. 195-211

[14] M.H. Carpenter; D. Gottlieb; S. Abarbanel Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes, J. Comput. Phys., Volume 111 (1994), pp. 220-236

[15] J.C. Hardin, J.R. Ristorcelli, C.K.W. Tam (Eds.), ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA), NASA Conference Publication 3300, 1995

[16] J. Westerlund, High order simulation of rocket launch noise, Master's Thesis, Uppsala University, Sweden, 2002

[17] B. Müller; J. Westerlund High order numerical simulation of rocket launch noise (G.C. Cohen; E. Heikkola; P. Joly; P. Neittaanmäki, eds.), Mathematical and Numerical Aspects of Wave Propagation, Springer-Verlag, Berlin, 2003, pp. 95-100

Cited by Sources:

Comments - Policy