Abstract
For the numerical solution of nonstationary quasilinear hyperbolic equations, a family of symmetric semidiscrete bicompact schemes based on collocation polynomials is constructed in the one- and multidimensional cases. A dispersion analysis of a semidiscrete bicompact scheme of six-order accuracy in space is performed. It is proved that the dispersion properties of the scheme are preserved on highly nonuniform spatial grids. It is shown that the phase error of the sixth-order bicompact scheme does not exceed 0.2% in the entire range of dimensionless wave numbers. A numerical example is presented that demonstrates the ability of the bicompact scheme to adequately simulate wave propagation on coarse grids at long times.
Similar content being viewed by others
References
T. Colonius and S. K. Lele, Prog. Aerosp. Sci. 40 (6), 345–416 (2004).
J. A. Ekaterinaris, Prog. Aerosp. Sci. 41 (3–4), 192–300 (2005).
K. A. Kurbatskii and R. R. Mankbadi, Int. J. Comput. Fluid Dyn. 18 (6), 533–546 (2004).
X. Liu, S. Zhang, H. Zhang, and C.-W. Shu, J. Comput. Phys. 248, 235–256 (2013).
C. Bogey and C. Bailly, J. Comput. Phys. 194 (1), 194–214 (2004).
B. V. Rogov and M. N. Mikhailovskaya, Dokl. Math. 84 (2), 747–752 (2011).
E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems (Springer-Verlag, Berlin, 1996; Mir, Moscow, 1999).
A. V. Chikitkin, Candidate’s Dissertation in Mathematics and Physics (MFTI, Dolgoprudnyi, 2016).
M. D. Bragin and B. V. Rogov, Dokl. Math. 95 (2), 140–143 (2017).
C. K. W. Tam, in Fourth Computational Aeroacoustics Workshop on Benchmark Problems (2004), NASA/CP-2004-212954.
L. M. Skvortsov, Mat. Model. 14 (2), 3–17 (2002).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Chikitkin, B.V. Rogov, 2017, published in Doklady Akademii Nauk, 2017, Vol. 476, No. 4, pp. 381–386.
Rights and permissions
About this article
Cite this article
Chikitkin, A.V., Rogov, B.V. A sixth-order bicompact scheme with spectral-like resolution for hyperbolic equations. Dokl. Math. 96, 480–485 (2017). https://doi.org/10.1134/S1064562417050192
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562417050192