Geodesic
High-accuracy finite-difference boundary conditions for two-dimensional aeroacoustic problems
Matematičeskoe modelirovanie, Tome 23 (2011) no. 11, pp. 131-154.

Voir la notice de l'article provenant de la source Math-Net.Ru

For high-accuracy finite-difference approximations to hyperbolic equations, namely, DRP scheme by Tam and Webb and its modifications by Bailly and Bogey, boundary conditions have been constructed. Starting from the 1D transport equation, the technique is extended to the Euler equations both in one and two dimensions. The cases of external (artificial) boundaries and rigid walls are considered.
Keywords: nonreflecting boundary conditions, finite differences, dispersion-relation-preserving scheme.
Mots-clés : Euler equations 
@article{MM_2011_23_11_a8,
     author = {L. W. Dorodnicyn},
     title = {High-accuracy finite-difference boundary conditions for two-dimensional aeroacoustic problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {131--154},
     publisher = {mathdoc},
     volume = {23},
     number = {11},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_11_a8/}
}
TY  - JOUR
AU  - L. W. Dorodnicyn
TI  - High-accuracy finite-difference boundary conditions for two-dimensional aeroacoustic problems
JO  - Matematičeskoe modelirovanie
PY  - 2011
SP  - 131
EP  - 154
VL  - 23
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2011_23_11_a8/
LA  - ru
ID  - MM_2011_23_11_a8
ER  - 
%0 Journal Article
%A L. W. Dorodnicyn
%T High-accuracy finite-difference boundary conditions for two-dimensional aeroacoustic problems
%J Matematičeskoe modelirovanie
%D 2011
%P 131-154
%V 23
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2011_23_11_a8/
%G ru
%F MM_2011_23_11_a8
L. W. Dorodnicyn. High-accuracy finite-difference boundary conditions for two-dimensional aeroacoustic problems. Matematičeskoe modelirovanie, Tome 23 (2011) no. 11, pp. 131-154. http://geodesic.mathdoc.fr/item/MM_2011_23_11_a8/

[1] C. K. W. Tam, J. C. Webb, “Dispersion-relation-preserving finite difference schemes for computational acoustics”, J. Comput. Phys., 107 (1993), 262–281 | DOI | MR | Zbl

[2] C. Bogey, C. Bailly, “A family of low dispersive and low dissipative explicit schemes for flow and noise computations”, J. Comput. Phys., 194 (2004), 194–214 | DOI | Zbl

[3] C. K. W. Tam, Zh. Dong., “Wall boundary conditions for high-order finite-difference schemes in computational aeroacoustics”, Theor. Comput. Fluid Dynamics, 6 (1994), 303–322 | DOI | Zbl

[4] J. Berland, C. Bogey, O. Marsden, C. Bailly, “High-order, low dispersive and low dissipative explicit schemes for multiple-scale and boundary problems”, J. Comput. Phys., 224 (2007), 637–662 | DOI | MR | Zbl

[5] J. W. Kim, “Optimised boundary compact finite difference schemes for computational aeroacoustics”, J. Comput. Phys., 225 (2007), 995–1019 | DOI | MR | Zbl

[6] V. S. Ryabenkii, “Tochnyi perenos raznostnykh kraevykh uslovii”, Funkts. analiz i ego prilozheniya, 24:3 (1990), 90–91 | MR

[7] V. S. Ryabenkii, V. I. Turchaninov, “Spektralnyi podkhod k postroeniyu neotrazhayuschikh iskusstvennykh granichnykh uslovii”, Matem. modelirovanie, 13:11 (2001), 23–47 | MR

[8] V. S. Ryabenkii, “Obschie konstruktsii raznostnykh neotrazhayuschikh iskusstvennykh granichnykh uslovii dlya nestatsionarnykh zadach”, Metod raznostnykh potentsialov i ego prilozheniya, 2-e izd., dopoln. i ispravl., FIZMATLIT, M., 2002, 409–452

[9] C. W. Rowley, T. Colonius, “Discretely nonreflecting boundary conditions for linear hyperbolic systems”, J. Comput. Phys., 157 (2000), 500–538 | DOI | MR | Zbl

[10] L. V. Dorodnitsyn, “Iskusstvennye granichnye usloviya pri chislennom modelirovanii dozvukovykh techenii gaza”, Zh. vychisl. matem. i matem. fiz., 45:7 (2005), 1251–1278 | MR | Zbl

[11] L. W. Dorodnicyn, “Artificial boundary conditions for high-accuracy aeroacoustic algorithms”, SIAM J. Scientific Computing, 32:4 (2010), 1950–1979 | DOI | MR | Zbl

[12] F. Q. Hu, M. Y. Hussaini, J. L. Manthey, “Low dissipation and dispersion Runge–Kutta Schemes for computational acoustics”, J. Comput. Phys., 124 (1996), 177–191 | DOI | MR | Zbl

[13] M. Calvo, J. M. Franco, L. Randez, “A new minimum storage Runge.Kutta scheme for computational acoustics”, J. Comput. Phys., 211 (2004), 1–12 | DOI | MR

[14] J. Berland, C. Bogey, C. Bailly, “Low-dissipation and low-dispersion fourth-order Runge–Kutta algorithm”, Comput. Fluids, 35 (2006), 1459–1463 | DOI | MR | Zbl

[15] L. N. Trefethen, “Group velocity in finite difference schemes”, SIAM Rev., 24 (1982), 113–136 | DOI | MR | Zbl

[16] A. N. Tikhonov, A. A. Samarskii, Uravneniya matematicheskoi fiziki, Izd-vo MGU, M., 1999 | MR

[17] B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves”, Math. Comput., 31 (1977), 629–651 | DOI | MR | Zbl

[18] S. V. Tsynkov, “Numerical solution of problems on unbounded domains. A review”, Appl. Numer. Math., 27:4 (1998), 465–532 | DOI | MR | Zbl

[19] G. Fibich, S. Tsynkov, “High-order two-way artificial boundary conditions for nonlinear wave propagation with backscattering”, J. Comput. Phys., 171:2 (2001), 632–677 | DOI | MR | Zbl

[20] S. V. Tsynkov, “Artificial boundary conditions for the numerical simulation of unsteady acoustic waves”, J. Comput. Phys., 189:2 (2003), 626–650 | DOI | MR | Zbl

[21] C. K. W. Tam, J. C. Webb, Zh. Dong, “A study of the short wave components in computational acoustics”, J. Comput. Acoustics, 1 (1993), 1–30 | DOI | MR

[22] C. K. W. Tam, “Benchmark problems and solutions”, ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics, NASA CP 3300, Hampton, VA, 1995, 1–13