A new numerical model for propagation of tsunami waves

Karel Švadlenka

Kybernetika (2007)

  • Volume: 43, Issue: 6, page 893-902
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Švadlenka, Karel. "A new numerical model for propagation of tsunami waves." Kybernetika 43.6 (2007): 893-902. <http://eudml.org/doc/33905>.

@article{Švadlenka2007,
abstract = {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.},
author = {Švadlenka, Karel},
journal = {Kybernetika},
keywords = {long waves; nonlinear hyperbolic equation; volume constraint; free boundary; variational method; discrete Morse semi-flow; FEM; long waves; volume constraint; variational method; discrete Morse semi-flow; FEM; coastal area; constrained hyperbolic free-boundary problem},
language = {eng},
number = {6},
pages = {893-902},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A new numerical model for propagation of tsunami waves},
url = {http://eudml.org/doc/33905},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Švadlenka, Karel
TI - A new numerical model for propagation of tsunami waves
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 6
SP - 893
EP - 902
AB - 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.
LA - eng
KW - long waves; nonlinear hyperbolic equation; volume constraint; free boundary; variational method; discrete Morse semi-flow; FEM; long waves; volume constraint; variational method; discrete Morse semi-flow; FEM; coastal area; constrained hyperbolic free-boundary problem
UR - http://eudml.org/doc/33905
ER -

References

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  1. Bona J. L., Chen M., Saut J.-C., 10.1007/s00332-002-0466-4, I: Derivation and linear theory. J. Nonlinear Sci. 12 (2002), 283–318 Zbl1059.35103MR1915939DOI10.1007/s00332-002-0466-4
  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 (1991) Zbl0850.76043MR1178095
  3. Nagasawa T., Omata S., Discrete Morse semiflows of a functional with free boundary, Adv. Math. Sci. Appl. 2 (1993), 147–187 (1993) Zbl0795.35150MR1239254
  4. Omata S., 10.1016/S0362-546X(97)00397-0, Nonlinear Anal. 30 (1997), 2181–2187 (1997) MR1490340DOI10.1016/S0362-546X(97)00397-0
  5. Švadlenka K., Omata S., Construction of weak solution to hyperbolic problem with volume constraint, Submitted to Nonlinear Anal 
  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 Zbl1122.35159MR2253225
  7. Yoshiuchi H., Omata S., Švadlenka, K., Ohara K., Numerical solution of film vibration with obstacle, Adv. Math. Sci. Appl. 16 (2006), 33–43 Zbl1122.35160MR2253223

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