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Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 1, Pages 170–184 (Mi zvmmf8054)  

This article is cited in 30 scientific papers (total in 30 papers)

Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows

O. V. Bulatova, T. G. Elizarovab

a Moscow State University, Moscow, 119992 Russia
b Institute for Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia

Abstract: Regularized shallow water equations are derived as based on a regularization of the Navier–Stokes equations in the form of quasi-gasdynamic and quasi-hydrodynamic equations. Efficient finite-difference algorithms based on the regularized shallow water equations are proposed for the numerical simulation of shallow water flows. The capabilities of the model are examined by computing a test Riemann problem, the flow over an obstacle, and asymmetric dam break.

Key words: quasi-gasdynamic and quasi-hydrodynamic equations, regularized shallow water equations, finite volume method.

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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:1, 160–173

Bibliographic databases:

UDC: 519.634
Received: 25.07.2010

Citation: O. V. Bulatov, T. G. Elizarova, “Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows”, Zh. Vychisl. Mat. Mat. Fiz., 51:1 (2011), 170–184; Comput. Math. Math. Phys., 51:1 (2011), 160–173

Citation in format AMSBIB
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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. Sheretov Yu.V., “Metody postroeniya tochnykh reshenii kvazigidrodinamicheskikh uravnenii”, Vestn. Tverskogo gos. un-ta. Ser. Prikladnaya matematika, 2011, no. 21, 5–26  mathnet  mathnet  elib
    2. Sheretov Yu.V., “Edinstvennost klassicheskogo resheniya osnovnoi nachalno-kraevoi zadachi dlya kvazigidrodinamicheskikh uravnenii”, Vestn. Tverskogo gos. un-ta. Ser. Prikladnaya matematika, 2011, no. 20, 7–20  mathnet  mathnet  elib
    3. Sheretov Yu.V., “Edinstvennost resheniya kvazigidrodinamicheskikh uravnenii v priblizhenii melkoi vody”, Vestn. Tverskogo gos. un-ta. Ser. Prikladnaya matematika, 2011, no. 22, 7–28  mathnet  mathnet  elib
    4. Elizarova T.G., Zlotnik A.A., Nikitina O.V., “Modelirovanie odnomernykh techenii melkoi vody na osnove regulyarizovannykh uravnenii”, Preprinty IPM im. M.V. Keldysha, 2011, no. 33, 1–36  elib
    5. T. G. Elizarova, A. A. Zlotnik, O. V. Nikitina, “Modelirovanie odnomernykh techenii melkoi vody na osnove regulyarizovannykh uravnenii”, Preprinty IPM im. M. V. Keldysha, 2011, 033, 36 pp.  mathnet
    6. Zlotnik A.A., “Spatial discretization of one-dimensional quasi-gasdynamic systems of equations and the entropy and energy balance equations”, Dokl. Math., 86:1 (2012), 464–468  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    7. A. A. Zlotnik, “O postroenii kvazigazodinamicheskikh sistem uravnenii i barotropnoi sistemy s potentsialnoi massovoi siloi”, Matem. modelirovanie, 24:4 (2012), 65–79  mathnet  mathscinet
    8. T. G. Elizarova, M. A. Istomina, N. K. Shelkovnikov, “Numerical simulation of the solitary wave generation in a wind-water circular tunnel”, Math. Models Comput. Simul., 4:6 (2012), 552–559  mathnet  crossref  elib
    9. A. A. Zlotnik, “Prostranstvennaya diskretizatsiya odnomernoi barotropnoi kvazigazodinamicheskoi sistemy uravnenii i uravnenie energeticheskogo balansa”, Matem. modelirovanie, 24:10 (2012), 51–64  mathnet  mathscinet
    10. Sukhomozgii A.A., Sheretov Yu.V., “Testirovanie novogo algoritma rascheta odnomernykh nestatsionarnykh techenii zhidkosti so svobodnoi granitsei”, Vestn. Tverskogo gos. un-ta. Ser. Prikladnaya matematika, 2012, no. 4, 47–64  mathnet  mathnet  elib
    11. Sukhomozgii A.A., Sheretov Yu.V., “Edinstvennost resheniya regulyarizovannykh uravnenii Sen-Venana v lineinom priblizhenii”, Vestn. Tverskogo gos. un-ta. Ser. Prikladnaya matematika, 2012, no. 1, 5–18  mathnet  elib
    12. T. G. Elizarova, D. S. Saburin, “Numerical modeling of liquid fluctuations in fuel tanks”, Math. Models Comput. Simul., 5:5 (2013), 470–478  mathnet  crossref
    13. M. O. Korpusov, E. V. Yushkov, “Solution blowup for systems of shallow-water equations”, Theoret. and Math. Phys., 177:2 (2013), 1505–1514  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. Khrapov S.S., Pisarev A.V., Kobelev I.A., Zhumaliev A.G., Agafonnikova E.O., Losev A.G., Khoperskov A.V., “The Numerical Simulation of Shallow Water: Estimation of the Roughness Coefficient on the Flood Stage”, Adv. Mech. Eng., 2013, 787016  crossref  isi  elib  scopus
    15. Elizarova T., Saburin D., “Matematicheskoe modelirovanie i vizualizatsiya techenii zhidkosti v gruzovoi emkosti gazovoza pri ego soudarenii s ledovym prepyatstviem”, Nauchnaya vizualizatsiya, 5:4 (2013), 118–135  elib
    16. V. V. Churuksaeva, M. D. Mikhailov, “Chislennoe modelirovanie potoka zhidkosti nad relefom dna”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2014, no. 1(27), 51–60  mathnet
    17. M. A. Istomina, E. V. Yushkov, “Roll waves in an annular channel”, Comput. Math. Math. Phys., 54:1 (2014), 123–134  mathnet  crossref  crossref  isi  elib  elib
    18. O. V. Bulatov, “Analytical and numerical Riemann solutions of the Saint Venant equations for forward- and backward-facing step flows”, Comput. Math. Math. Phys., 54:1 (2014), 158–171  mathnet  crossref  crossref  isi  elib  elib
    19. T. G. Elizarova, O. V. Bulatov, “Chislennyi algoritm resheniya regulyarizovannykh uravnenii melkoi vody na nestrukturirovannykh setkakh”, Preprinty IPM im. M. V. Keldysha, 2014, 021, 27 pp.  mathnet
    20. V. A. Balashov, E. B. Savenkov, “Fenomenologicheskii vyvod kvazigidrodinamicheskoi sistemy uravnenii s uchetom ob'emnoi vyazkosti”, Preprinty IPM im. M. V. Keldysha, 2015, 068, 25 pp.  mathnet
    21. V. A. Balashov, E. B. Savenkov, “Numerical study of a quasi-hydrodynamic system of equations for flow computation at small mach numbers”, Comput. Math. Math. Phys., 55:10 (2015), 1743–1751  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    22. Elizarova T.G., Saburin D.S., “the Numerical Simulation of Faraday Waves on the Basis of Hydrodynamic Equations in the Shallow-Water Approximation”, Mosc. Univ. Phys. Bull., 70:1 (2015), 1–6  crossref  isi  scopus
    23. A. A. Zlotnik, “On conservative spatial discretizations of the barotropic quasi-gasdynamic system of equations with a potential body force”, Comput. Math. Math. Phys., 56:2 (2016), 303–319  mathnet  crossref  crossref  isi  elib
    24. O. V. Bulatov, T. G. Elizarova, “Regularized shallow water equations for numerical simulation of flows with a moving shoreline”, Comput. Math. Math. Phys., 56:4 (2016), 661–679  mathnet  crossref  crossref  mathscinet  isi  elib
    25. V. A. Balashov, A. A. Zlotnik, E. B. Savenkov, “Issledovanie barotropnoi kvazigidrodinamicheskoi modeli dvukhfaznoi smesi s uchetom poverkhnostnykh effektov”, Preprinty IPM im. M. V. Keldysha, 2016, 089, 25 pp.  mathnet  crossref
    26. Zlotnik A. Gavrilin V., “On a Conservative Finite-Difference Method for 1D Shallow Water Flows Based on Regularized Equations”, Mathematical Problems in Meteorological Modelling, Mathematics in Industry, 24, ed. Batkai A. Csomos P. Farago I. Horanyi A. Szepszo G., Springer Int Publishing Ag, 2016, 3–18  crossref  mathscinet  zmath  isi
    27. T. G. Elizarova, D. S. Saburin, “Application of the regularized shallow water equations for numerical simulation of casavie fluctuations in the Azov sea”, Math. Models Comput. Simul., 9:4 (2017), 423–436  mathnet  crossref  elib
    28. Saburin D.S. Elizarova T.G., “Modelling the Azov Sea Circulation and Extreme Surges in 2013-2014 Using the Regularized Shallow Water Equations”, Russ. J. Numer. Anal. Math. Model, 33:3 (2018), 173–185  crossref  mathscinet  zmath  isi  scopus
    29. T. G. Elizarova, A. V. Ivanov, “Regularized equations for numerical simulation of flows in the two-layer shallow water approximation”, Comput. Math. Math. Phys., 58:5 (2018), 714–734  mathnet  crossref  crossref  isi  elib
    30. T. G. Elizarova, A. V. Ivanov, “Metod regulyarizatsii dlya chislennogo modelirovaniya perenosa primesi v melkoi vode”, Preprinty IPM im. M. V. Keldysha, 2019, 027, 28 pp.  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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