Article information
2014 , Volume 19, ¹ 6, p.19-41
Gusev O.I.
Algorithm for surface waves calculation above a movable bottom within the frame of plane nonlinear dispersive model
The influence of the effects due to frequency dispersion on tsunami wave patterns is investigated. The numerical algorithm developed is based on the partitioning of the fully nonlinear dispersive shallow water equations with a movable bottom into elliptic and hyperbolic subproblems, which are solved alternately at each time step. At that, equations of the hyperbolic subproblem differ from the classic shallow water system in the right side only. Therefore, well-examined finite-difference schemas are implemented for both subproblems. In this paper, we describe in detail the integro-interpolation method for the elliptic subproblem. The hyperbolic subproblem is solved by the explicit schema of predictorcorrector type. For open bounds of the computational region Zommerfeld type conditions are proposed for both subproblems. Obtained numerical solutions are compared with computations based on shallow water model and experimental data. Regarding the problem of disintegration of initial disturbance above the flat bottom, it is checked out that as the source width is decreased so dispersion is significantly increased. During the simulations of the landslide-generated tsunamis, we detect the loss of adequacy of the model when the ratio of the landslide length to its depth is small. In other cases the model reproduce wave pattern better than the classic shallow water model. In addition, significant dependence of the surface wave amplitudes versus the landslide width is demonstrated. Good agreement of numerical solutions with experimental data obtained in the problem of interaction of solitary wave with the conical island shows the applicability of the model in complex multi linked domains.
[full text] Keywords: Underwater landslide, surface waves, tsunami, shallow water equations, nonlinear dispersive equations, numerical simulation, finite-difference schema
Author(s): Gusev Oleg Igorevitch PhD. Position: Senior Research Scientist Office: Federal Research Center for Information and Computational Technologies Address: 630090, Russia, Novosibirsk, 6, Acad. Lavrentjev avenue
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Bibliography link: Gusev O.I. Algorithm for surface waves calculation above a movable bottom within the frame of plane nonlinear dispersive model // Computational technologies. 2014. V. 19. ¹ 6. P. 19-41
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