Abstract
In this paper a brief survey of finite difference methods and time discretization schemes for the numerical simulation of problems in Computational Aero Acoustics (CAA), with special emphasis in the contributions of the authors in the last years to the subject, is presented. Due to the specific properties of these problems it is shown by means of some illustrative examples that standard schemes have some drawbacks and new numerical schemes have been derived taking into account not only the usual stability and accuracy requirements but also the dissipation and dispersion properties as well as low storage requirements. Some relevant contributions to the subject are presented comparing the relative merits by means of a Fourier analysis and numerical experiments.
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References
J. Berland, C. Bogey, O. Marsden and C. Bailly. High-order, low dispersive and low dissipative explicit schemes for multiple-scale and boundary problems J. of Comput. Phys. 224,2, 637–662 (2007).
V. Allampalli, R. Hixon, M. Nallasamy and S.D. Sawyer. High-accuracy large-step explicit Runge-Kutta (HALE-RK) schemes for computational aeroacoustics J. Comput. Phys. 228, 3837–3850 (2009).
C. Bogey and C. Bailly. A family of low dispersive and low dissipative explicit schemes for flow and noise computations J. Comput. Phys. 194, 194–214 (2004).
M. Calvo, J.M. Franco, J.I. Montijano and L. Rández. Minimum Storage Runge-Kutta Schemes for Computational Accoustics Computers and Math. with Applications 45, pp. 535–545 (2003).
M. Calvo, J.M. Franco and L. Rández. A new minimum storage Runge-Kutta scheme for computational accoustics J. Comput. Phys. 201, pp. 1–12 (2004).
M. Calvo, J.M. Franco, J.I. Montijano and L. Rández. Optimization of spatial and minimum storage RK schemes for computational acoustics Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2009. AIP Conference Proceedings, 1168 743–745 (2009).
M. H. Carpenter and C. A. Kennedy. A Fourth-Order 2N-Storage Runge-Kutta Scheme NASA TR TM109112, June 1994.
F. Q. Hu, M. Y. Hussaini and J. Manthey. Low-dissipation and low dispersion Runge-Kutta schemes for computational accoustics J. Comput. Phys. 124, 177–191 (1996).
C. A. Kennedy M. H. Carpenter and R. M. Lewis. Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations NASA/CR-1999-209349, ICASE Report (99) (1999).
J.L. Mead and R.A. Renaut. Optimal Runge-Kutta Methods for First Order Pseudospectral Operators J. Comput. Phys. 152, 404–419 (1999).
J. Ramboer, T. Broeckhoven, S. Smirnov and C. Lacor. Optimization of time integration schemes coupled to spatial discretization for use in CAA applications J. Comput. Phys. 213, 777–802 (2006).
D. Stanescu and W. G. Habashi. 2N-Storage Low dissipation and Dispersion Runge-Kutta schemes for Computational Accoustics J. Comput. Phys. 143, 674–681 (1998).
C.K.W. Tam and J.C. Webb. Dispersion-relation-preserving finite difference schemes for computational acoustics J. Comput. Phys. 107, 262 (1993).
J.H. Williamson. Low-storage Runge-Kutta schemes J. Comput. Phys. 35, 48 (1980).
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This work was supported by project MTM2007-67530-C02-01
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Calvo, M., Franco, J.M., Montijano, J.I. et al. Highly stable RK time advancing schemes for Computational Aero Acoustics. SeMA 50, 83–98 (2010). https://doi.org/10.1007/BF03322543
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DOI: https://doi.org/10.1007/BF03322543