Matematicheskoe modelirovanie
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Model.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Matematicheskoe modelirovanie, 1998, Volume 10, Number 12, Pages 107–123 (Mi mm1352)  
This article is cited in 29 scientific papers (total in 29 papers)

Computational methods and algorithms

Nonlinear correction of Cabaret scheme

V. M. Goloviznin, S. A. Karabasov

Nuclear Safety Institute, RAS
Full-text PDF (1541 kB) Citations (29)
Abstract: The paper presents a conservative algorithm of nonlinear correction for new three layer second order Cabaret scheme with a space split time derivative, which possesses enhanced dispersion and diffusion properties. The properties of the new algorithm are illustrated through sets of computational runs, where the algorithm is demonstrated to provide monotonicity of evolving solution with big space variations profiles. After comparison with positive nonlinear second order TVD and UNO schemes it is concluded that the new method enables to obtain sufficiently more accurate solution. The new method is used for solution of hyperbolic equations system following from two-phase filtration of immiscible fluids problem in the Backley–Laverett model.
Received: 26.08.1998
Language: Russian
Citation: V. M. Goloviznin, S. A. Karabasov, “Nonlinear correction of Cabaret scheme”, Mat. Model., 10:12 (1998), 107–123
Citation in format AMSBIB
\Bibitem{GolKar98}
\by V.~M.~Goloviznin, S.~A.~Karabasov
\paper Nonlinear correction of Cabaret scheme
\jour Mat. Model.
\yr 1998
\vol 10
\issue 12
\pages 107--123
\mathnet{http://mi.mathnet.ru/mm1352}
Linking options:
  • https://www.mathnet.ru/eng/mm1352
  • https://www.mathnet.ru/eng/mm/v10/i12/p107
    • This publication is cited in the following 29 articles:
    1. I. V. Popov, “Method for constructing high-order approximation schemes for hyperbolic equations”, Math. Models Comput. Simul., 16:6 (2024), 853–860  mathnet  crossref  crossref
    2. V. Goloviznin, Petr Mayorov, Pavel Mayorov, A. Solovjev, N. Afanasiev, “Explicit numerical algorithm for non-hydrostatic fluid dynamics equations based on the CABARET scheme”, Math. Models Comput. Simul., 15:6 (2023), 1008–1023  mathnet  crossref  crossref  mathscinet
    3. N. A. Afanasiev, V. M. Goloviznin, V. N. Semenov, A. M. Sipatov, S. S. Nesterov, “Direct simulation of thermoacoustic instability in gas generators using “CABARET” scheme”, Math. Models Comput. Simul., 13:5 (2021), 820–830  mathnet  crossref  crossref
    4. M. I. Ivanov, I. A. Kremer, Yu. M. Laevskii, “Ob odnoi protivopotokovoi skheme resheniya zadachi filtratsii”, Sib. elektron. matem. izv., 16 (2019), 757–776  mathnet  crossref
    5. K. M. Sergeenko, V. M. Goloviznin, V. Yu. Glotov, “LES-simulation of heat transfer in a turbulent pipe flow with lead coolant at different Reynolds numbers”, Math. Models Comput. Simul., 11:2 (2019), 176–189  mathnet  crossref
    6. A. V. Danilin, A. V. Solovjev, “Application of the CABARET algorithm for modeling turbulent mixing on the example of the Richtmyer–Meshkov instability”, Math. Models Comput. Simul., 11:2 (2019), 247–255  mathnet  crossref
    7. V. M. Goloviznin, V. A. Isakov, “Balance-characteristic scheme as applied to the shallow water equations over a rough bottom”, Comput. Math. Math. Phys., 57:7 (2017), 1140–1157  mathnet  crossref  crossref  isi  elib
    8. Cherevko A.A., Gologush T.S., Petrenko I.A., Ostapenko V.V., “Numerical Modeling Process of Embolization Arteriovenous Malformation”, Proceedings of the XXV Conference on High-Energy Processes in Condensed Matter (HEPCM 2017), AIP Conference Proceedings, 1893, ed. Fomin V., Amer Inst Physics, 2017, UNSP 030123-1  crossref  isi  scopus
    9. Usov E.V., Sorokin A.A., Chukhno V.I., Mosunova N.A., “Modeling of Oxide Layer Formation and Corrosion Products Coagulation and Transport in Lead Coolant Using the Oxid Module of the Hydra-Ibrae/Lm Code”, Atom. Energy, 122:3 (2017), 172–177  crossref  isi  scopus
    10. Kulikov I., Vorobyov E., “Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows”, J. Comput. Phys., 317 (2016), 318–346  crossref  mathscinet  zmath  isi  elib  scopus
    11. V. Yu. Glotov, V. M. Goloviznin, “CABARET scheme in velocity-pressure formulation for two-dimensional incompressible fluids”, Comput. Math. Math. Phys., 53:6 (2013), 721–735  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    12. N. N. Galanina, V. A. Isakov, N. N. Tyurina, A. P. Favorskiy, “The constructive approach to the numerical solution of quasi-linear advection equations”, Math. Models Comput. Simul., 6:2 (2014), 155–161  mathnet  crossref  mathscinet
    13. Yu. M. Laevsky, T. A. Kandryukova, “On approximation of discontinuous solutions to the Buckley–Leverett equation”, Num. Anal. Appl., 5:3 (2012), 222–230  mathnet  crossref  elib
    14. V. M. Goloviznin, A. A. Kanaev, “High-resolution numerical algorithm for one-dimensional scalar conservation laws with a constrained solution”, Comput. Math. Math. Phys., 52:3 (2012), 400–410  mathnet  crossref  zmath  adsnasa  isi  elib  elib
    15. A. V. Danilin, V. M. Goloviznin, “Cabaret scheme in “velocity–vorticity” formulation for numerical modeling of ideal fluid motion in two-dimensional domain”, Math. Models Comput. Simul., 4:6 (2012), 574–586  mathnet  crossref  mathscinet  elib
    16. V. M. Goloviznin, A. A. Kanaev, “The principle of minimum of partial local variations for determining convective flows in the numerical solution of one-dimensional nonlinear scalar hyperbolic equations”, Comput. Math. Math. Phys., 51:5 (2011), 824–839  mathnet  crossref  mathscinet  isi
    17. V. Yu. Glotov, V. M. Goloviznin, “Сabaret scheme for the two-dimensional incompressible fluid in terms of «stream function – vorticity»”, Math. Models Comput. Simul., 4:2 (2012), 144–154  mathnet  crossref  mathscinet
    18. P. G. Yakovlev, S. A. Karabasov, V. M. Goloviznin, “Direct simulation of interacting vortex pairs”, Math. Models Comput. Simul., 4:3 (2012), 288–296  mathnet  crossref  mathscinet
    19. Abakumov M.V., Galanina A.M., Isakov V.A., Tyurina N.N., Favorskii A.P., Khrulenko A.B., “Quasi-Acoustic Scheme for the Euler Equations of Gas Dynamics”, Differ Equ, 47:8 (2011), 1103–1109  crossref  mathscinet  zmath  isi  elib  elib  scopus
    20. S. V. Kostrykin, “About one variant of multidimensional extension of the “cabaret” scheme”, Math. Models Comput. Simul., 2:5 (2010), 564–573  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математическое моделирование
    Statistics & downloads:
    Abstract page:1333
    Full-text PDF :562
    First page:3
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025