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

Gayaz Khakimzyanov; Nina Yu Shokina; Denys Dutykh; Dimitrios Mitsotakis

doi:10.1016/j.cam.2015.12.004

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

Gayaz Khakimzyanov, Nina Yu Shokina, Denys Dutykh, Dimitrios Mitsotakis

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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 in several important practical examples. Finally, the simulation results are compared with the well-known analytical and experimental predictions.

Original language	British English
Pages (from-to)	82-96
Number of pages	15
Journal	Journal of Computational and Applied Mathematics
Volume	298
DOIs	https://doi.org/10.1016/j.cam.2015.12.004
State	Published - 15 May 2016

Keywords

Asymptotic expansion
Finite differences
Finite volumes
Nonlinear shallow water equations
Wave run-up

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10.1016/j.cam.2015.12.004

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title = "A new run-up algorithm based on local high-order analytic expansions",

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 in several important practical examples. Finally, the simulation results are compared with the well-known analytical and experimental predictions.",

keywords = "Asymptotic expansion, Finite differences, Finite volumes, Nonlinear shallow water equations, Wave run-up",

author = "Gayaz Khakimzyanov and Shokina, {Nina Yu} and Denys Dutykh and Dimitrios Mitsotakis",

note = "Funding Information: This research was supported by RSCF Project No. 14-17-00219. D. Dutykh acknowledges the support of the Dynasty Foundation as well as the hospitality of the Institute of Computational Technologies SB RAS during his visit in October 2014. This work was finalized later at the Institute f{\"u}r Analysis, Johannes Kepler Universit{\"a}t Linz whose hospitality is equally acknowledged. D. Mitsotakis was supported by the Marsden Fund administered by the Royal Society of New Zealand . All the authors would like to thank the anonymous Referee for very helpful suggestions on their manuscript. Publisher Copyright: {\textcopyright} 2015 Elsevier B.V. All rights reserved.",

year = "2016",

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doi = "10.1016/j.cam.2015.12.004",

language = "British English",

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AU - Khakimzyanov, Gayaz

AU - Shokina, Nina Yu

AU - Dutykh, Denys

AU - Mitsotakis, Dimitrios

N1 - Funding Information: This research was supported by RSCF Project No. 14-17-00219. D. Dutykh acknowledges the support of the Dynasty Foundation as well as the hospitality of the Institute of Computational Technologies SB RAS during his visit in October 2014. This work was finalized later at the Institute für Analysis, Johannes Kepler Universität Linz whose hospitality is equally acknowledged. D. Mitsotakis was supported by the Marsden Fund administered by the Royal Society of New Zealand . All the authors would like to thank the anonymous Referee for very helpful suggestions on their manuscript. Publisher Copyright: © 2015 Elsevier B.V. All rights reserved.

PY - 2016/5/15

Y1 - 2016/5/15

N2 - 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 in several important practical examples. Finally, the simulation results are compared with the well-known analytical and experimental predictions.

AB - 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 in several important practical examples. Finally, the simulation results are compared with the well-known analytical and experimental predictions.

KW - Asymptotic expansion

KW - Finite differences

KW - Finite volumes

KW - Nonlinear shallow water equations

KW - Wave run-up

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DO - 10.1016/j.cam.2015.12.004

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SN - 0377-0427

VL - 298

SP - 82

EP - 96

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

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

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Keywords

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