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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki

Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 4, Pages 665–684 (Mi zvmmf10381)

Regularized shallow water equations for numerical simulation of flows with a moving shoreline
O. V. Bulatov, T. G. Elizarova

References

1. Stoker Dzh. Dzh., Volny na vode. Matematicheskaya teoriya i prilozheniya, IL, M., 1959
2. Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001
3. Levin B. W., Nosov M. A., Physics of tsunamis, Springer, 2008
4. Elizarova T. G., Bulatov O. V., “Regularized shallow water equations and a new method of simulation of the open channel flows”, Int. J. Comp. and Fluids, 46 (2011), 206–211  crossref  mathscinet  zmath
5. Bulatov O. V., Elizarova T. G., “Regulyarizovannye uravneniya melkoi vody i effektivnyi metod chislennogo modelirovaniya techenii v neglubokikh vodoemakh”, Zh. vychisl. matem. i matem. fiz., 51:1 (2011), 170–184  mathnet  mathscinet  zmath  elib
6. Elizarova T. G., Kvazigazodinamicheskie uravneniya i metody rascheta vyazkikh techenii, Nauchnyi mir, M., 2007
7. Sheretov Yu. V., Dinamika sploshnykh sred pri prostranstvenno-vremennom osrednenii, NITs “Regulyarnaya i khaoticheskaya dinamika”, M.–Izhevsk, 2009
8. 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, 033, 36 pp.  mathnet
9. Elizarova T. G., Istomina M. A., Shelkovnikov N. K., “Chislennoe modelirovanie formirovaniya uedinennoi volny v koltsevom aerogidrokanale”, Matem. modelirovanie, 24:4 (2012), 107–116  mathnet  elib
10. Bulatov O. V., “Analiticheskie i chislennye resheniya uravnenii Sen-Venana dlya nekotorykh zadach o raspade razryva nad ustupom i stupenkoi dna”, Zh. vychisl. matem. i matem. fiz., 54:1 (2014), 150–163  mathnet  isi
11. Elizarova T. G., Saburin D. A., “Chislennoe modelirovanie kolebanii zhidkosti v toplivnykh bakakh”, Matem. modelirovanie, 25:3 (2013), 75–88  mathnet  zmath  isi  elib
12. Elizarova T. G., Saburin D. S., “Chislennoe modelirovanie voln Faradeya na osnove uravnenii gidrodinamiki v priblizhenii melkoi vody”, Vestnik Mosk. un-ta. Ser. 3. Fizika i astronomiya, 2015, no. 1, 3–8
13. Zlotnik A. A., “O postroenii kvazigazodinamicheskikh sistem uravnenii i barotropnoi sistemy s potentsialnoi massovoi siloi”, Matem. modelirovanie, 24:4 (2012), 65–79  mathnet  mathscinet  elib
14. Zlotnik A. A., “Energeticheskie ravenstva i otsenki dlya barotropnykh kvazigazo- i kvazigidrodinamicheskikh sistem uravnenii”, Zh. vychisl. matem. i matem. fiz., 50:2 (2010), 325–337  mathnet  mathscinet  zmath  isi  elib
15. Zlotnik A. A., Chetverushkin B. N., “Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them”, Comput. Math. and Math. Phys., 48:3 (2008), 445–472  mathnet  crossref  mathscinet  zmath
16. 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(24), 5–17  mathnet
17. 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(27), 47–64  mathnet  mathscinet
18. Elizarova T. G., Bulatov O. V., “Chislennyi algoritm resheniya regulyarizovannykh uravnenii melkoi vody na nestrukturirovannykh setkakh”, Preprinty IPM im. M. V. Keldysha, 2014, 021, 27 pp.  mathnet
19. Elizarova T. G., Istomina M. A., “Kvazigazodinamicheskii algoritm resheniya uravnenii melkoi vody v polyarnoi sisteme koordinat”, Preprinty IPM im. M. V. Keldysha, 2014, 065, 24 pp.  mathnet
20. LeVeque R. J., “Balancing source terms and flux gradients in high-resolution godunov methods: the quasi-steady wave propogation algorithm”, J. Comput. Phys., 146:1 (1998), 346–365  crossref  mathscinet  zmath  isi
21. Huang Y., Zhang N., Pei Y., “Well-balanced finite volume scheme for shallow water flooding and drying over arbitrary topography”, Engineering Appl. of Computat. Fluid Mech., 7:1 (2013), 40–54  isi
22. Zlotnik A. A., “O konservativnykh prostranstvennykh diskretizatsiyakh barotropnoi kvazigazodinamicheskoi sistemy uravnenii s potentsialnoi massovoi siloi”, Zh. vychisl. matem. i matem. fiz., 56:2 (2016), 301–318  mathnet  crossref  elib
23. Ricchiuto M., Abgrall R., Deconinck H., “Application of conservative residual distribution schemes to the solution of the shallow water equations on unstructured meshes”, J. Comput. Phys., 222 (2007), 287–331  crossref  mathscinet  zmath  isi  elib
24. Birman A., Falcovitz J., “Application of the GRP scheme to open channel flow equations”, J. Comput. Phys., 222 (2007), 131–154  crossref  mathscinet  zmath  isi  elib
25. Petrosyan A. S., Dopolnitelnye glavy gidrodinamiki tyazheloi zhidkosti so svobodnoi granitsei, Mekhanika, upravlenie, informatika, IKI RAN, M., 2010
26. Kun Xu, “A well-ballanced gas-kinetic scheme for the shallow-water equations with source terms”, J. Comput. phys., 178 (2002), 533–562  crossref  mathscinet  zmath  isi
27. Marche F., Theoretical and numerical study of shallow water models. Application to nearstore hydrodynamics, PhD thesis, Universite de Bordeau 1, 2005 http://www.math.u-bordeau1.fr/marche/THESE/marche.pdf
28. Carrier G. F., Greenspan H. P., “Water waves of finite amplitude on a sloping beach”, J. Fluid Mech., 4 (1958), 97–109  crossref  mathscinet  zmath
29. Carrier G. F., Wu T. T., Yeh H., “Tsunami run-up and draw-down on a plane beach”, J. Fluid Mechanics, 475 (2003), 79–99  crossref  mathscinet  zmath  isi
30. Benchmark problem № 1. Tsunami Runup onto a plane beach, http://isec.nacse.org/workshop/2004_cornell/bmark1.html
31. NOAA Center for tsunami research. Tsunami Runup onto a Complex Three-dimensional Beach. Monai Valley, http://nctr.pmel.noaa.gov/benchmark/Laboratory/Laboratory_MonaiValley/index.html
32. Ricchiuto M., “An explicit residual based approach for shallow water flows”, J. Comput. Phys., 280 (2015), 306–344  crossref  mathscinet  isi


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