An approximation algorithm for the treatment of sound points in the CABARET scheme

Authors

  • V.M. Goloviznin Lomonosov Moscow State University
  • A.V. Solovjev Nuclear Safety Institute (IBRAE) of RAS
  • V.A. Isakov Lomonosov Moscow State University

DOI:

https://doi.org/10.26089/NumMet.v17r215

Keywords:

systems of hyperbolic equations, shallow water equations with bottom topography, numerical methods, sound point, CABARET scheme

Abstract

A new numerical approach to the calculation of flux variables on a new time layer in the CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) scheme for the numerical solution of quasilinear hyperbolic differential equations is described. This approach allows one to uniformly treat all cases of sound points and does not violate the time reversibility properties of difference schemes in the absence of nonlinear correction of fluxes.

Author Biographies

V.M. Goloviznin

A.V. Solovjev

V.A. Isakov

References

  1. B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics (Nauka, Moscow, 1978; Amer. Math. Soc., Providence, 1983).
  2. A. G. Kulikovskii, N. V. Pogorelov, and A. Y. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Fizmztlit, Moscow, 2001; CRCC Press, Boca Raton, 2001).
  3. A. I. Zhukov, “Application of the Method of Characteristics to the Numerical Solution of One-Dimensional Problems of Gas Dynamics,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 58, 3-150 (1960).
  4. K. M. Magomedov and A. S. Kholodov, Grid-Characteristic Numerical Methods (Nauka, Moscow, 1988) [in Russian].
  5. M. A. Tolstykh, A Global Semi-Lagrangian Numerical Weather Prediction Model (OAO FOP, Obninsk, 2010) [in Russian].
  6. M. A. Tolstykh and V. V. Shashkin, “Vorticity-Divergence Mass-Conserving Semi-Lagrangian Shallow-Water Model Using the Reduced Grid on the Sphere,” J. Comput. Phys. 231 (11), 4205-4233 (2012).
  7. V. M. Goloviznin, S. A. Karabasov, and I. M. Kobrinskii, “Balance-Characteristic Schemes with Separated Conservative and Flux Variables,” Mat. Model. 15 (9), 29-48 (2003).
  8. V. M. Goloviznin, M. A. Zaitsev, S. A. Karabasov, and I. A. Korotkin, New CFD Algorithms for Multiprocessor Computer Systems (Mosk. Gos. Univ., Moscow, 2013) [in Russian].
  9. V. M. Goloviznin and S. A. Karabasov, “Nonlinear Correction of Cabaret Scheme,” Mat. Model. 10 (12), 107-123 (1998).
  10. A. Harten, “High Resolution Schemes for Hyperbolic Conservation Laws,” J. Comput. Phys. 49 (3), 357-393 (1983).
  11. V. M. Goloviznin, S. A. Karabasov, and V. G. Kondakov, “Generalization of CABARET Scheme for Two-Dimensional Orthogonal Computational Grids,” Mat. Model. 25 (7), 103-136 (2013) [Math. Models Comput. Simul. 6 (1), 56-79 (2014)].
  12. G. A. Faranosov, V. M. Goloviznin, S. A. Karabasov, et al., “CABARET Method on Unstructured Hexahedral Grids for Jet Noise Computation,” Comput. Fluids 88, 165-179 (2013).
  13. D. G. Asfandiyarov, V. M. Goloviznin, and S. A. Finogenov, “Parameter-Free Method for Computing the Turbulent Flow in a Plane Channel in a Wide Range of Reynolds Numbers,” Zh. Vychisl. Mat. Mat. Fiz. 55 (9), 1545-1558 (2015) [Comput. Math. Math. Phys. 55 (9), 1515-1526 (2015)].
  14. V. Yu. Glotov, V. M. Goloviznin, S. A. Karabasov, and A. P. Markeshteijn, “New Two-Level Leapfrog Scheme for Modeling the Stochastic Landau-Lifshitz Equations,” Zh. Vychisl. Mat. Mat. Fiz. 54 (2), 298-317 (2014) [Comput. Math. Math. Phys. 54 (2), 315-334 (2014)].

Published

26-04-2016

How to Cite

Головизнин В., Соловьев А., Исаков В. An Approximation Algorithm for the Treatment of Sound Points in the CABARET Scheme // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2016. 17. 166-176. doi 10.26089/NumMet.v17r215

Issue

Section

Section 1. Numerical methods and applications

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