ACOUSTIC PROPAGATION EVALUATION USING TRADITIONAL FINITE DIFFERENCES AND DISPERSION RELATION PRESERVING (DRP)

ACOUSTIC PROPAGATION EVALUATION USING TRADITIONAL FINITE DIFFERENCES AND DISPERSION RELATION PRESERVING (DRP)

Mainieri Junior, Paulo Alfredo; Oliveira, Odenir de; Silveira Neto, Aristeu da

Artigo Completo:

The main purpose of this work is the evaluation of spatial schemes used on CAA (Computational AeroAcoustic): Traditional finite differences, and DRP (Dispersion Relation Preserving), on 1D (one dimension) acoustic propagation prediction. A secondary goal is to present details of construction of DRP, proposed by Tam and Webb (1993) and advantages of this schemes over traditional finite differences schemes. Temporal schemes as Euler, Runge-Kutta 2nd and 4th order methods and CAA optimized methods such as LDDRK and RK46-NL will be evaluated. This work shows an outstanding efficiency of Runge-Kutta 2nd order over Runge-Kutta 4th order scheme, and in some cases, even superior to the optimized CAA schemes. The simulations revealed that DRP loss efficiency over traditional finite differences scheme when grid refinement occurs.

The main purpose of this work is the evaluation of spatial schemes used on CAA (Computational AeroAcoustic): Traditional finite differences, and DRP (Dispersion Relation Preserving), on 1D (one dimension) acoustic propagation prediction. A secondary goal is to present details of construction of DRP, proposed by Tam and Webb (1993) and advantages of this schemes over traditional finite differences schemes. Temporal schemes as Euler, Runge-Kutta 2nd and 4th order methods and CAA optimized methods such as LDDRK and RK46-NL will be evaluated. This work shows an outstanding efficiency of Runge-Kutta 2nd order over Runge-Kutta 4th order scheme, and in some cases, even superior to the optimized CAA schemes. The simulations revealed that DRP loss efficiency over traditional finite differences scheme when grid refinement occurs.

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DOI: 10.5151/mathpro-cnmai-0026

Referências bibliográficas

• [1] Berland, Julien, Bogey, Christophe, Bailly, Christophe, 2006, “Low-Dissipation and Low-Dispersion Fourth-Order Runge–Kutta Algorithm”, Computers Andamp; Fluids, 35, p. 1459–1463.
• [2] Hu, F. Q., Hussaini, M. Y., Manthey, J. L., 1996, “Low-Dissipation and Low-Dispersion Runge–Kutta Schemes for Computational Acoustics”, Journal of Computation Physics.124, p. 177- 191.
• [3] Mainieri, P.A. Jr, Almeida, O., Silveira, A. N., 2013, “Avaliação da Propagação Acústica Utilizando Diferenças Finitas Tradicionais e DRP”, Tese de Mestrado, Universidade Federal de Uberlândia, Uberlândia.
• [4] Tam, C. K. W., Webb, J. C., 1993, “Dipersion-Relation-Preserving Finite Difference Schemes for Computational Acoustic”, Journal of Computation Physics, 107, p. 262- 281.
• [5] Zhang, X., Blaisdell, G. A., Lyrintzis, A. S., December 2004, “High-Order Compact Schemes With Filters on Multi- block Domains”, Journal of Scientific Computing, Vol. 21, No. 3.

Como citar:

Mainieri Junior, Paulo Alfredo; Oliveira, Odenir de; Silveira Neto, Aristeu da; "ACOUSTIC PROPAGATION EVALUATION USING TRADITIONAL FINITE DIFFERENCES AND DISPERSION RELATION PRESERVING (DRP)", p-121-130. In: Anais do Congresso Nacional de Matemática Aplicada à Indústria [= Blucher Mathematical Proceedings, v.1, n.1]. São Paulo: Blucher, 2015.
ISSN soon, DOI 10.5151/mathpro-cnmai-0026