Geodesic
A numerical algorithm for computing tsunami wave amplitude
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 2, pp. 153-165

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A numerical algorithm for computing tsunami wave front amplitude is proposed. The first step consists in solving an appropriate eikonal equation. The eikonal equation is solved by the Godunov approach and the bicharacteristic method. The qualitative comparison of the two above methods is described. Then a change in variables associated with the eikonal solution is introduced. At the last step, using the expansion of the fundamental solution of shallow water equations in the sum of singular and regular parts, we obtain the Cauchy problem for the wave amplitude. This approach allows one to reduce computer costs. The numerical results are presented. 
@article{SJVM_2016_19_2_a2,
     author = {S. I. Kabanikhin and O. I. Krivorotko},
     title = {A numerical algorithm for computing tsunami wave amplitude},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {153--165},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2016_19_2_a2/}
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S. I. Kabanikhin; O. I. Krivorotko. A numerical algorithm for computing tsunami wave amplitude. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 2, pp. 153-165. http://geodesic.mathdoc.fr/item/SJVM_2016_19_2_a2/