A numerical algorithm for computing tsunami wave amplitudes

A numerical multistep algorithm for computing tsunami wave front amplitudes is proposed. The first step consists in solving an appropriate eikonal equation. The eikonal equation is solved with Godunov’s approach and a bicharacteristic method. A qualitative comparison of the two methods is done. A ch...

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Bibliographic Details
Published in:Numerical analysis and applications Vol. 9; no. 2; pp. 118 - 128
Main Authors: Kabanikhin, S. I., Krivorot’ko, O. I.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.04.2016
Subjects:
Mathematics
Mathematics and Statistics
Numerical Analysis
tsunami amplitude
finite difference approach
fundamental solution
eikonal equation
shallow water equations
ISSN:1995-4239, 1995-4247
Online Access:Get full text
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Summary:A numerical multistep algorithm for computing tsunami wave front amplitudes is proposed. The first step consists in solving an appropriate eikonal equation. The eikonal equation is solved with Godunov’s approach and a bicharacteristic method. A qualitative comparison of the two methods is done. A change of variables is made with the eikonal equation solution at the second step. At the last step, using an expansion of the fundamental solution to the shallow water equations in the new variables, we obtain a Cauchy problem of lesser dimension for the leading edge wave amplitude. The results of numerical experiments are presented.
ISSN:1995-4239
1995-4247
DOI:10.1134/S1995423916020038