DOI: https://doi.org/10.26089/NumMet.v23r423

Conservative-characteristic method for solving hyperbolic systems of equations on triangular computational grids

Authors

  • Vasily M. Goloviznin
  • Daniil Y. Gorbachev
  • Nikita A. Afanasiev

Keywords:

conservative-characteristic methods
CABARET method
computational fluid dynamics
shallow water
triangular computational grids

Abstract

This article considers a conservative-characteristic numerical method for solving hyperbolic systems of equations on triangular computational grids. The main steps of the algorithm are described with the example of solving two-dimensional shallow water equations. The method is verified and compared with the methods developed by other authors on the main tests for shallow water equations over a flat bottom.

Downloads

Published

2022-12-12

Issue

Vol. 23 (2022): Issue 4.

Section

Methods and algorithms of computational mathematics and their applications

Author Biographies

Vasily M. Goloviznin

Lomonosov Moscow State University
• Professor

Daniil Y. Gorbachev

Lomonosov Moscow State University
• PhD Student

Nikita A. Afanasiev

Lomonosov Moscow State University
• PhD Student

References

  1. D. C. Kutov, A. V. Sulimov, and V. B. Sulimov, “Supercomputer Docking: Investigation of Low Energy Minima of Protein-Ligand Complexes,” Supercomput. Front. Innovs. 5 (3), 134-137 (2018).
    doi 10.14529/jsfi180326.
  2. K. K. Abgaryan and M. A. Posypkin, “Optimization Methods as Applied to Parametric Identification of Interatomic Potentials,” Zh. Vychisl. Mat. Mat. Fiz. 54 (12), 1994-2001 (2014) [Comput. Math. Math. Phys. 54 (12), 1929-1935 (2014)].
    doi 10.1134/S0965542514120021.
  3. Yu. G. Yevtushenko, S. A. Lurie, M. A. Posypkin, and Yu. O. Solyaev, “Application of Optimization Methods for Finding Equilibrium States of Two-Dimensional Crystals,” Zh. Vychisl. Mat. Mat. Fiz. 56 (12), 2032-2041 (2016) [Comput. Math. Math. Phys. 56 (12), 2001-2010 (2016)].
    doi 10.1134/S0965542516120083.
  4. J. D. Pintér (Ed.), Global Optimization: Scientific and Engineering Case Studies (Springer, New York, 2006).
  5. I. Gubaydullin, L. Enikeeva, K. Barkalov, and I. Lebedev, “Parallel Global Search Algorithm for Optimization of the Kinetic Parameters of Chemical Reactions,” in Communications in Computer and Information Science (Springer, Cham, 2021), Vol. 1510, pp. 198-211.
    doi 10.1007/978-3-030-92864-3_16
  6. Ya. D. Sergeev and D. E. Kvasov, Diagonal Methods of Global Optimization (Fizmatlit, Moscow, 2008) [in Russian].
  7. R. Paulavicius and J. Zilinskas, Simplicial Global Optimization (Springer, New York, 2014).
    doi 10.1007/978-1-4614-9093-7.
  8. R. G. Strongin and Ya. D. Sergeyev, Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms (Springer, Berlin, 2000).
  9. Ya. D. Sergeyev, R. G. Strongin, and D. Lera, Introduction to Global Optimization Exploiting Space-Filling Curves (Springer, New York, 2013).
    doi 10.1007/978-1-4614-8042-6.
  10. R. G. Strongin, V. P. Gergel, V. A. Grishagin, and K. A. Barkalov, Parallel Computations in Global Optimization Problems (Mosk. Gos. Univ., Moscow, 2013) [in Russian].
  11. V. Sovrasov, “Comparison of Several Stochastic and Deterministic Derivative-Free Global Optimization Algorithms,” in Lecture Notes in Computer Science (Springer, Cham, 2019), Vol. 11548, pp. 70-81.
    doi 10.1007/978-3-030-22629-9_6.
  12. A. V. Boreskov, A. A. Kharlamov, N. D. Markovsky, et al., Parallel Computing on the GPU. Architecture and Programming Model of CUDA (Mosk. Gos. Univ., Moscow, 2015) [in Russian].
  13. A. S. Tanenbaum and T. Austin, Structured Computer Organization (Pearson, New York, 2006; Piter, Saint Petersburg, 2014).
  14. D. A. Komolov, R. A. Myalk, A. A. Zobenko, and A. S. Filippov, Computer-Aided Design Systems from Altera MAX+Plus II and Quartus II (RadioSoft, Moscow, 2002) [in Russian].
  15. V. Gergel, K. Barkalov, and A. Sysoyev, “Globalizer: A Novel Supercomputer Software System for Solving Time-Consuming Global Optimization Problems,” Numer. Algebra Control Optim. 8 (1), 47-62 (2018).
    doi 10.3934/naco.2018003.

License

Copyright (c) 2022 В. М. Головизнин, Д. Ю. Горбачев, Н.А. Афанасьев

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.