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Title: A new numerical model for propagation of tsunami waves (English)
Author: Švadlenka, Karel
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 43
Issue: 6
Year: 2007
Pages: 893-902
Summary lang: English
Category: math
Summary: A new model for propagation of long waves including the coastal area is introduced. This model considers only the motion of the surface of the sea under the condition of preservation of mass and the sea floor is inserted into the model as an obstacle to the motion. Thus we obtain a constrained hyperbolic free-boundary problem which is then solved numerically by a minimizing method called the discrete Morse semi-flow. The results of the computation in 1D show the adequacy of the proposed model. (English)
Keyword: long waves
Keyword: nonlinear hyperbolic equation
Keyword: volume constraint
Keyword: free boundary
Keyword: variational method
Keyword: discrete Morse semi-flow
Keyword: FEM
MSC: 35L70
MSC: 35R35
MSC: 47J30
MSC: 58E50
MSC: 74J15
MSC: 76B15
MSC: 86A05
idZBL: Zbl 1140.35529
idMR: MR2388402
Date available: 2009-09-24T20:30:56Z
Last updated: 2013-09-21
Stable URL:
Reference: [1] Bona J. L., Chen M., Saut J.-C.: Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media.I: Derivation and linear theory. J. Nonlinear Sci. 12 (2002), 283–318 Zbl 1059.35103, MR 1915939, 10.1007/s00332-002-0466-4
Reference: [2] Kikuchi N.: An approach to the construction of Morse flows for variational functionals.In: Nematics – Mathematical and Physical Aspects (J. M. Coron, J. M. Ghidaglia, and F. Hélein, eds.), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 332 (1991), Kluwer Academic Publishers, Dodrecht – Boston – London, pp. 195–198 Zbl 0850.76043, MR 1178095
Reference: [3] Nagasawa T., Omata S.: Discrete Morse semiflows of a functional with free boundary.Adv. Math. Sci. Appl. 2 (1993), 147–187 Zbl 0795.35150, MR 1239254
Reference: [4] Omata S.: A numerical method based on the discrete Morse semiflow related to parabolic and hyperbolic equations.Nonlinear Anal. 30 (1997), 2181–2187 MR 1490340, 10.1016/S0362-546X(97)00397-0
Reference: [5] Švadlenka K., Omata S.: Construction of weak solution to hyperbolic problem with volume constraint.Submitted to Nonlinear Anal
Reference: [6] Yamazaki T., Omata S., Švadlenka, K., Ohara K.: Construction of approximate solution to a hyperbolic free boundary problem with volume constraint and its numerical computation.Adv. Math. Sci. Appl. 16 (2006), 57–67 Zbl 1122.35159, MR 2253225
Reference: [7] Yoshiuchi H., Omata S., Švadlenka, K., Ohara K.: Numerical solution of film vibration with obstacle.Adv. Math. Sci. Appl. 16 (2006), 33–43 Zbl 1122.35160, MR 2253223


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