A new run-up algorithm based on local high-order analytic expansions

G. Khakimzyanov; N. Shokina; D. Dutykh; D. Mitsotakis

doi:10.1016/j.cam.2015.12.004

2016

A new run-up algorithm based on local high-order analytic expansions

JJ. Comp. Appl. Math.

G. Khakimzyanov, N. Shokina, D. Dutykh and D. Mitsotakis

J. Comp. Appl. Math. 298: 82-96 (2016)

Open Access

HAL Version DOI

Abstract

The practically important problem of the wave run-up is studied in this article in the framework of Nonlinear Shallow Water Equations (NSWE). The main novelty consists in the usage of high order local asymptotic analytical solutions in the vicinity of the shoreline. Namely, we use the analytical techniques introduced by S. Kovalevskaya and the analogy with the compressible gas dynamics (i.e. gas outflow problem into the vacuum). Our run-up algorithm covers all the possible cases of the wave slope on the shoreline and it incorporates the new analytical information in order to determine the shoreline motion to higher accuracy. The application of this algorithm is illustrated on several important practical examples. Finally, the simulation results are compared with the well-known analytical and experimental predictions.

Keywords

wave run-upasymptotic expansionfinite volumesonlinear shallow water equationsfinite differences

Bibliographic record

Journal: J. Comp. Appl. Math.

Volume: 298

Pages: 82-96

DOI: 10.1016/j.cam.2015.12.004

HAL: hal-01084811

BibTeX Citation

@article{Khakimzyanov2016runupalgorithm,
  author = {Khakimzyanov, G. and Shokina, N. and Dutykh, D. and Mitsotakis, D.},
  title = {A new run-up algorithm based on local high-order analytic expansions},
  journal = {J. Comp. Appl. Math.},
  year = {2016},
  volume = {298},
  pages = {82--96},
  doi = {10.1016/j.cam.2015.12.004},
  abstract = {The practically important problem of the wave run-up is studied in this article in the framework of Nonlinear Shallow Water Equations (NSWE). The main novelty consists in the usage of high order local asymptotic analytical solutions in the vicinity of the shoreline. Namely, we use the analytical techniques introduced by S. Kovalevskaya and the analogy with the compressible gas dynamics (i.e. gas outflow problem into the vacuum). Our run-up algorithm covers all the possible cases of the wave slope on the shoreline and it incorporates the new analytical information in order to determine the shoreline motion to higher accuracy. The application of this algorithm is illustrated on several important practical examples. Finally, the simulation results are compared with the well-known analytical and experimental predictions.},
  keywords = {wave run-up, asymptotic expansion, finite volumes, onlinear shallow water equations, finite differences}
}