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Mathematical Models and Computer Simulations

, Volume 2, Issue 5, pp 564–573 | Cite as

A variant of the multidimensional generalization of the cabaret scheme

  • S. V. Kostrykin
Article
  • 32 Downloads

Abstract

To solve the advection equation in divergent form, a new variant of the conservative multidimensional extension of the cabaret scheme is proposed. In the two-dimensional case, the two- and three-layered variants of the scheme are derived on a rectangular grid. The stability properties of the scheme and its dissipative and dispersion characteristics are analyzed. The results of the numerical tests show the robustness of the proposed scheme and the improved accuracy compared to the leapfrog scheme. This scheme is compared with the known multidimensional extension of the cabaret scheme, and further possibilities for its improvement are discussed.

Keywords

Flux Variable Rectangular Grid Advection Equation Conservative Variable Courant Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J. P. Boris, D. L. Book, and K. Hain, “Flux-Corrected Transport: Generalization of the Method,” J. Comput. Phys. 31, 335–350 (1975).Google Scholar
  2. 2.
    A. Iserles, “Generalized Leapfrog Methods,” IMA J. Num. Anal. 6(4), 381–392 (1986).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    J. P. Thomas and P. L. Roe, “Development of Non-Dissipative Numerical Schemes for Computational Aero-Acoustics,” in AIAA 11th Computational Fluid Dynamics Conf. (Orlando, 1993)Google Scholar
  4. 4.
    V. M. Goloviznin and A. A. Samarskii, “Difference Approximation of Convection Transport with Spatial Splitting of Time Derivative,” Mat. Model. 10, No. 1, 86–100 (1998).MATHMathSciNetGoogle Scholar
  5. 5.
    V. M. Goloviznin and A. A. Samarskii, “Nelineinaya korrektsiya skhemy kabare,” Mat. Model. 10, No. 12, 107–123 (1998).MathSciNetGoogle Scholar
  6. 6.
    C. Kim, “Accurate Multi-Level Schemes for Advection,” Int. J. Numer. Meth. Fluids 41, 471–494 (2003).MATHCrossRefGoogle Scholar
  7. 7.
    Q. H. Tran and B. Scheurer, “High-Order Monotonicity-Preserving Compact Schemes for Linear Scalar Advection on 2D Irregular Meshes,” J. Comput. Phys, 175, 454–486 (2002).MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    S. A. Karabasov and V. M. Goloviznin, “A New Efficient High-Resolution Method for Non-Linear Problems in Aeroacoustics,” AIAA J. 45, No. 12, 2861–2871 (2007).CrossRefGoogle Scholar
  9. 9.
    V. M. Goloviznin, V. N. Semenov, I. A. Korotkin, and S. A. Karabasov, “A Novel Computational Method for Modeling Stochastic Advection in Heterogeneous Media,” Transport in Porous Media 66(3), 439–456 (2007).CrossRefMathSciNetGoogle Scholar
  10. 10.
    V. M. Goloviznin, S. A. Karabasov, and I. M. Kobrinskii, “Balance-Characteristic Schemes with Separated Conservative and Flow Variables,” Mat. Model. 15, No. 9, 29–48 (2003).MATHMathSciNetGoogle Scholar
  11. 11.
    S. V. Kostrykin, “The Way to Choose an Optimal Transfer Scheme for WAM-4 Model of Wind Wave,” Vych. Tekhnol. 13,Special Issue 3, 80–90 (2008).Google Scholar
  12. 12.
    J. Thuburn, “Multidimensional Flux-Limited Advection Schemes,” J. Comput. Phys. 123, 74–83 (1996).MATHCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • S. V. Kostrykin
    • 1
  1. 1.Institute of Numerical MathematicsRussian Academy of SciencesMoscowRussia

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