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Num. Meth. Prog., 2011, Volume 12, Issue 2, Pages 282–297 (Mi vmp195)  

This article is cited in 19 scientific papers (total in 19 papers)

Вычислительные методы и приложения

A numerical scheme for simulating the dynamics of surface water on the basis of the combined SPH-TVD approach

S. S. Khrapov, A. V. Khoperskov, N. M. Kuz'min, A. V. Pisarev, I. A. Kobelev

Volgograd State University

Abstract: A new numerical algorithm is developed for calculating the shallow water dynamics. The algorithm provides a cross-cutting computation on irregular or/and discontinuous reliefs with unsteady boundaries of the “water-dry bottom” type. The method is based on the combination of modified SPH and TVD approaches for the shallow water equations. A large number of classical problems is tested. The numerical results show that the combined SPH-TVD scheme is conservative, well-balanced, has the second order of accuracy on smooth solutions. This scheme has the first order of accuracy in the domains containing discontinuities of the flow parameters and kinks of the relief profile.

Keywords: shallow water equations; numerical scheme; SPH; TVD; irregular bottom topography.

Full text: PDF file (8176 kB)
UDC: 519.6

Citation: S. S. Khrapov, A. V. Khoperskov, N. M. Kuz'min, A. V. Pisarev, I. A. Kobelev, “A numerical scheme for simulating the dynamics of surface water on the basis of the combined SPH-TVD approach”, Num. Meth. Prog., 12:2 (2011), 282–297

Citation in format AMSBIB
\Bibitem{KhrKhoKuz11}
\by S.~S.~Khrapov, A.~V.~Khoperskov, N.~M.~Kuz'min, A.~V.~Pisarev, I.~A.~Kobelev
\paper A numerical scheme for simulating the dynamics of surface water
on the basis of the combined SPH-TVD approach
\jour Num. Meth. Prog.
\yr 2011
\vol 12
\issue 2
\pages 282--297
\mathnet{http://mi.mathnet.ru/vmp195}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Khoperskov, S. S. Khrapov, A. V. Pisarev, A. A. Voronin, M. V. Eliseeva, I. A. Kobelev, “Zadacha upravleniya gidrologicheskim rezhimom v ekologo-ekonomicheskoi sisteme “Volzhskaya GES – Volgo-Akhtubinskaya poima”. Ch. 1. Modelirovanie dinamiki poverkhnostnykh vod v period vesennego pavodka”, Probl. upravl., 5 (2012), 18–25  mathnet
    2. A. V. Pisarev, S. S. Khrapov, E. O. Agafonnikova, A. V. Khoperskov, “Chislennaya model dinamiki poverkhnostnykh vod v rusle Volgi: otsenka koeffitsienta sherokhovatosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 1, 114–130  mathnet
    3. N. M. Kuzmin, A. V. Belousov, T. S. Shushkevich, S. S. Khrapov, “Chislennaya skhema cSPH — TVD: issledovanie vliyaniya ogranichitelei naklonov”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2014, no. 1(20), 22–33  mathnet
    4. T. A. Dyakonova, A. V. Pisarev, A. V. Khoperskov, S. S. Khrapov, “Matematicheskaya model dinamiki poverkhnostnykh vod”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2014, no. 1(20), 35–44  mathnet
    5. M. V. Eliseeva, A. V. Pisarev, “Veb-orientirovannaya sistema podgotovki tsifrovoi modeli relefa mestnosti”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2014, no. 1(20), 46–51  mathnet
    6. A. L. Shantyr, “Lineinyi analiz modelei melkoi vody s uchetom neodnorodnosti dna”, Mezhdunar. nauch.-issled. zhurn., 2014, no. 4(23), 72–76  mathnet
    7. A. V. Kofanov, V. D. Liseikin, A. D. Rychkov, “Application of coordinate transformations in numerical simulation of tsunami runup by the large particle method”, Comput. Math. Math. Phys., 55:1 (2015), 109–116  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    8. E. V. Bochkareva, S. S. Khrapov, “Chislennoe modelirovanie dinamiki zvukovykh voln v aktivnykh sredakh s ispolzovaniem skhemy MUSCL”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 1(26), 13–22  mathnet  crossref
    9. A. V. Belousov, S. S. Khrapov, “Razrabotka programmy dlya chislennogo gazodinamicheskogo modelirovaniya na osnove lagranzhevo-eilerovoi skhemy LES — ASG”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 1(26), 30–39  mathnet  crossref
    10. T. S. Shushkevich, N. M. Kuzmin, M. A. Butenko, “Trekhmernyi parallelnyi chislennyi gazodinamicheskii kod na osnove smeshannogo lagranzhevo-eilerova podkhoda”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 4(29), 24–34  mathnet  crossref
    11. A. V. Belousov, S. S. Khrapov, “Modelirovanie gazodinamicheskikh techenii na osnove lagranzhevo-eilerovoi skhemy LES — ASG”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 5(30), 36–51  mathnet  crossref
    12. A. A. Voronin, A. A. Vasilchenko, O. S. Yakushkina, “Kognitivnyi analiz i stsenarno-imitatsionnoe modelirovanie razvitiya ekologo-ekonomicheskoi situatsii v severnoi chasti Volgo-Akhtubinskoi poimy”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 6(31), 17–30  mathnet  crossref
    13. A. G. Losev, A. V. Khoperskov, A. S. Astakhov, Kh. M. Suleimanova, “Problemy izmereniya i modelirovaniya teplovykh i radiatsionnykh polei v biotkanyakh: analiz dannykh mikrovolnovoi termometrii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 6(31), 31–71  mathnet  crossref
    14. A. A. Voronin, A. A. Vasilchenko, A. V. Pisarev, S. S. Khrapov, Yu. E. Radchenko, “Proektirovanie mekhanizmov upravleniya gidrologicheskim rezhimom Volgo-Akhtubinskoi poimy na osnove geoinformatsionnogo i gidrodinamicheskogo modelirovaniya”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 1(32), 24–37  mathnet  crossref
    15. T. A. Dyakonova, S. S. Khrapov, A. V. Khoperskov, “Problema granichnykh uslovii dlya uravnenii melkoi vody”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:3 (2016), 401–417  mathnet  crossref  mathscinet  elib
    16. S. S. Khrapov, N. M. Kuzmin, M. A. Butenko, “Sravnenie tochnosti i skhodimosti dlya metoda CSPH — TVD i nekotorykh eilerovykh skhem dlya resheniya uravnenii gazodinamiki”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 6(37), 166–173  mathnet  crossref
    17. E. O. Agafonnikova, A. Yu. Klikunova, A. V. Khoperskov, “Computer simulation of the Volga river hydrological regime: problem of water-retaining dam optimal location”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:3 (2017), 148–155  mathnet  crossref  elib
    18. V. S. Bakulin, A. A. Vasilchenko, A. A. Voronin, M. A. Kharitonov, “Optimizatsiya i stsenarno-imitatsionnoe modelirovanie dinamiki struktury malykh iskusstvennykh rusel poimennykh territorii”, Matematicheskaya fizika i kompyuternoe modelirovanie, 20:4 (2017), 26–38  mathnet  crossref
    19. D. V. Sadin, “Analiz dissipativnykh svoistv gibridnogo metoda krupnykh chastits dlya strukturno slozhnykh techenii gaza”, Kompyuternye issledovaniya i modelirovanie, 12:4 (2020), 757–772  mathnet  crossref
  • Numerical methods and programming
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