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A Coupled Model for Wave Run-up Simulation

Part of:Basic methods in fluid mechanicsIncompressible inviscid fluids

Published online by Cambridge University Press:  31 January 2018

Iryanto and
S.R. Pudjaprasetya
Iryanto*
Affiliation:
Informatics Department, Politeknik Negeri Indramayu, Indramayu, Indonesia
S.R. Pudjaprasetya*
Affiliation:
Mathematics Department, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia
*
*Corresponding author. Email addresses:iryanto.math@yahoo.com (Iryanto), sr_pudjap@math.itb.ac.id (S. R. Pudjaprasetya)
*Corresponding author. Email addresses:iryanto.math@yahoo.com (Iryanto), sr_pudjap@math.itb.ac.id (S. R. Pudjaprasetya)

Abstract

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Simplified models like the shallow water equations (SWE) are commonly adopted for describing a wide range of free surface flow problems, like flows in rivers, lakes, estuaries, or coastal areas. In the literature, numerical methods for the SWE are mostly mesh-based. However, this macroscopic approach is unable to accurately represent the complexity of flows near coastlines, where waves nearly break. This fact prompted the idea of coupling the mesh-based SWE model with a meshless particle method for solving the Euler equations. In a previous paper, a method to couple the staggered scheme SWE and the smoothed particle hydrodynamics (SPH) Euler equations was developed and discussed. In this article, this coupled model is used for simulating solitary wave run-up on a sloping beach. The results show strong agreement with the experimental data of Synolakis. Simulations of wave overtopping over a seawall were also performed.

Keywords

Smoothed particle hydrodynamicsstaggered conservative schemesolitary wave runupwave overtopping

MSC classification

Secondary:76M28: Particle methods and lattice-gas methods76M10: Finite element methods76B25: Solitary waves

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 4 , November 2017, pp. 728 - 740
Copyright
Copyright © Global-Science Press 2017 

References

[1] Becker, M. and Teschner, M., Weakly compressible SPH for free surface flows, in Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation, pp. 209–217, Eurographics Association, 2007.Google Scholar
[2] Didenkulova, I. and Pelinovsky, E., Run-up of long waves on a beach: The influence of the incident wave form, Oceanology, 48 (2008), 1–6.Google Scholar
[3] Gomez-Gesteira, M., Rogers, B. D., Crespo, A. J., Dalrymple, R., Narayanaswamy, M., and Dominguez, J. M., SPHysics–development of a free-surface fluid solver–part 1: Theory and formulations, Computers & Geosciences, 48 (2012), 289–299.Google Scholar
[4] Iryanto, , Shallow water - Navier-Stokes coupling method in ocean wave simulation, in International Symposium on Computational Science, pp. 56–68, 2015.Google Scholar
[5] Kassiotis, C., Ferrand, M., Violeau, D., Rogers, B., Stansby, P. and Benoit, M., Coupling SPH with a 1-D Boussinesq-type wave model, in 6th International SPHERIC Workshop, pp. 241–247, 2011.Google Scholar
[6] Katell, G. and Eric, B., Accuracy of solitary wave generation by a piston wave maker, J. Hydraul. Res., 40 (2002), 321–331.Google Scholar
[7] Liu, G.-R. and Liu, M. B., Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific, 2003.Google Scholar
[8] Mahmoudi, A., Hakimzadeh, H. and Ketabdari, M. J., Simulation of wave propagation over coastal structures using WCSPH method, Journal of Marine Engineering, 2 (2014), 1–13.Google Scholar
[9] Monaghan, J. J., Simulating free surface flows with SPH, J. Comput. Phys., 110 (1994), 399–406.Google Scholar
[10] Monaghan, J. J., Smoothed particle hydrodynamics, Annu. Rev. Astron. Astrophys., 30 (1992), 543–574.Google Scholar
[11] Narayanaswamy, M., Crespo, A. J. C., M. Gómez-Gesteira and Dalrymple, R. A., SPHysics-FUNWAVE hybrid model for coastal wave propagation, J. Hydraul. Res., 48 (2010), 85–93.Google Scholar
[12] De Padova, D., Dalrymple, R. A. and Mossa, M., Analysis of the artificial viscosity in the smoothed particle hydrodynamics modelling of regular waves, J. Hydraul. Res., 52 (2014), 836–848.Google Scholar
[13] Pudjaprasetya, S. R. and I.Magdalena, Momentum conservative schemes for shallow water flows, East Asian J. Appl. Math., 4 (2014), 152–165.Google Scholar
[14] Stelling, G. S. and Duinmeijer, S. A., A staggered conservative scheme for every Froude number in rapidly varied shallow water flows, International Journal for Numerical Methods in Fluids, 43 (2003), 1329–1354.Google Scholar
[15] Stelling, G. and Zijlema, M., An accurate and efficient finite-difference algorithm for nonhydrostatic free-surface flow with application to wave propagation, International Journal for Numerical Methods in Fluids, 43 (2003), 1–23.Google Scholar
[16] Synolakis, C. E., The runup of solitary waves, Journal of FluidMechanics, 185 (1987), 523–545.Google Scholar
[17] Synolakis, C. E., Bernard, E. N., Titov, V. V., U. Kânoğlu and F. González, Standards, criteria, and procedures for NOAA evaluation of tsunami numerical models: Seattle, Washington, NOAA/Pacific Marine Environmental Laboratory, tech. rep., Technical Memorandum OAR PMEL-135, 2007.Google Scholar
[18] The NOAA Center for Tsunami Research, Solitary wave on a canonical beach, http://nctr.pmel.noaa.gov/benchmark/Laboratory/Laboratory_CanonicalBathymetry/index.html, accessed on 18 September 2015.Google Scholar