Инд. авторы:	Fedotova Z.I., Khakimzyanov G.S.
Заглавие:	Characteristics of finite difference methods for dispersive shallow water equations
Библ. ссылка:	Fedotova Z.I., Khakimzyanov G.S. Characteristics of finite difference methods for dispersive shallow water equations // Russian Journal of Numerical Analysis and Mathematical Modelling. - 2016. - Vol.31. - Iss. 3. - P.149-158. - ISSN 0927-6467. - EISSN 1569-3988.
Внешние системы:	DOI: 10.1515/rnam-2016-0015; РИНЦ: 27109403; SCOPUS: 2-s2.0-84973481461; WoS: 000377580300003;
Реферат:	eng: The paper contains a description of the most important properties of numerical methods for solving nonlinear dispersive hydrodynamic equations and their distinctions from similar properties of finite difference schemes approximating classic dispersion-free shallow water equations. © 2016 Walter de Gruyter GmbH, Berlin/Boston.
Ключевые слова:	accuracy; dispersion; finite difference methods; Nonlinear equations; Shallow water equations; Nonlinear dispersive equations; Nonlinear dispersive; Hydrodynamic equations; Finite difference scheme; Numerical methods; Finite difference method; Equations of motion; Dispersions; Dispersion (waves); Convergence of numerical methods; stability; Nonlinear dispersive equations; accuracy;
Издано:	2016
Физ. характеристика:	с.149-158
Цитирование:	1. M. B. Abbott, H. M. Petersen, and O. Skovgaard, On the numerical modelling of short waves in shallow water. J. Hydraulic Res. 16 (1978), No. 3, 173-204. 2. M. E. Alexander and J. Ll Morris, Galerkin methods applied to some model equations for non-linear dispersive waves. J. Comput. Phys. 30 (1979), 428-451. 3. T. B. Benjamin, J. L. Bona, and J. J. Mahony, Model equations for long waves in nonlinear dispersive systems. Philosophical Transactions of the Royal Society of London. A. 272 (1972), 47-78. 4. J. C. Eilbeck and G. R. McGuire, Numerical study of the regularized long-wave equations 1: Numerical methods. J. Comput. Phys. 19 (1975), 43-57. 5. R. C. Ertekin, W. C. Webster, and J. V. Wehausen, Waves caused by a moving disturbance in a shallow channel of finite width. J. Fluid Mech. 169 (1986), 275-292. 6. Z. I. Fedotova and G. S. Khakimzyanov, Shallow water equations on a movable bottom. Russ. J. Numer. Anal. Math. Modelling 24 (2009), No. 1, 31-42. 7. Z. I. Fedotova and G. S. Khakimzyanov, The basic nonlinear-dispersive hydrodynamic model of long surface waves. Comp. Tech. 19 (2014), No. 6, 77-94 (In Russian). 8. Z. I. Fedotova, G. S. Khakimzyanov, and D. Dutykh, Energy equation for certain approximate models of long-wave hydrodynamics. Russ. J. Numer. Anal. Math. Modelling 29 (2014), No. 3, 167-178. 9. Z. I. Fedotova, G. S. Khakimzyanov, and O. I. Gusev, History of the development and analysis of numerical methods for solving nonlinear dispersive equations of hydrodynamics. I. One-dimensional models problems. Comp. Tech. 20 (2015), No. 5, 120-156 (In Russian). 10. Z. I. Fedotova and V. Yu. Pashkova, Methods of construction and the analysis of difference schemes for nonlinear dispersive models of wave hydrodynamics. Russ. J. Numer. Anal. Math. Modelling 12 (1997), No. 2, 127-149. 11. S. Glimsdal, G. K. Pedersen, K. Atakan, C. B. Harbitz, H. P. Langtangen, and F. Lovholt, Propagation of the Dec. 26, 2004, Indian Ocean Tsunami: Effects of dispersion and source characteristics. International J. Fluid Mech. Res. 33 (2006), No. 1, 15-43. 12. J. Grue, E. N. Pelinovsky, D. Fructus, T. Talipova, and C. Kharif, Formation of undular bores and solitary waves in the Strait of Malacca caused by the 26 December 2004 Indian Ocean tsunami. J. Geophys. Res. 113 (2008), C05008. 13. O. I. Gusev and G. S. Khakimzyanov, Numerical simulation of long surface waves on a rotating sphere within the framework of the full nonlinear dispersive model. Comp. Tech. 20 (2015), No. 3, 3-32 (in Russian). 14. G. S. Khakimzyanov, O. I. Gusev, S. A. Beisel, L. B. Chubarov, and N. Yu. Shokina, Simulation of tsunami waves generated by submarine landslides in the Black Sea. Russ. J. Numer. Anal. Math. Modelling 30 (2015), No. 4, 227-237. 15. G. S. Khakimzyanov, Yu. I. Shokin, V. B. Barakhnin, and N. Yu. Shokina, Numerical Simulation of Fluid Flows with Surface Waves. Sib. Branch, Russ. Acad. Sci., Novosibirsk, 2001 (in Russian). 16. L. A. Kompaniets, Analysis of difference algorithms for nonlinear dispersive shallow water models. Russ. J. Numer. Anal. Math. Modelling 11 (1996), No. 3, 205-222. 17. F. Lovholt and G. Pedersen, Instabilities of Boussinesq models in non-uniform depth. Int. J. Numer. Meth. Fluids 61 (2009), 606-637. 18. O. Nwogu, Alternative form of Boussinesq equations for nearshore wave propagation. J. Waterway Port Coastal Ocean Engrg. 119 (1993), No. 6, 618-638. 19. D. H. Peregrine, Calculations of the development of an undular bore. J. Fluid Mech. 25 (1966), part 2, 321-331. 20. D. H. Peregrine, Long waves on a beach. J. Fluid Mech. 27 (1967), part 4, 815-827. 21. B. L. Rozhdestvenskiy and N. N. Yanenko, Systems of Quasilinear Equations and Their Application to Gas Dynamics. Nauka, Moscow, 1968 (In Russian). 22. O. B. Rygg, Nonlinear refraction-diffraction of surface waves in intermediate and shallow water. Coastal Engrg. J. 12 (1988), No. 3, 191-211. 23. Yu. I. Shokin, The Method of Differential Approximation. Springer-Verlag, Berlin, 1983. 24. Yu. I. Shokin, Z. I. Fedotova, and G. S. Khakimzyanov, Hierarchy of nonlinear models of the hydrodynamics of long surface waves. Doklady Physics 60 (2015), No. 5, 224-228. 25. G. Wei and J. T. Kirby, Time-dependent numerical code for extended Boussinesq equations. J. Waterway Port Coastal Ocean Engrg. 121 (1995), No. 5, 251-261. 26. G. Wei, J. T. Kirby, S. T. Grilli, and R. Subramanya, A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves. J. Fluid Mech. 294 (1995), 71-92. 27. M. I. Zheleznyak and E. N. Pelinovsky, Physico-mathematical models of the tsunami climbing a beach. In: Tsunami Climbing a Beach (Ed. E. N. Pelinovsky). IAP Akad. Sci. USSR, Gorky, 1985, pp. 8-33 (in Russian).