{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T03:20:06Z","timestamp":1777951206352,"version":"3.51.4"},"reference-count":50,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computer Physics Communications"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.cpc.2026.110098","type":"journal-article","created":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T16:13:42Z","timestamp":1771863222000},"page":"110098","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["HOS-Ocean v2.1: Extensions of a nonlinear wave solver based on the High-Order Spectral method"],"prefix":"10.1016","volume":"323","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5937-4504","authenticated-orcid":false,"given":"Guillaume","family":"Ducrozet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-9333-673X","authenticated-orcid":false,"given":"Moran","family":"Charlou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7574-1773","authenticated-orcid":false,"given":"F\u00e9licien","family":"Bonnefoy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.cpc.2026.110098_bib0001","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1017\/S002211208700288X","article-title":"A high-order spectral method for the study of nonlinear gravity waves","volume":"184","author":"Dommermuth","year":"1987","journal-title":"J. Fluid Mech."},{"issue":"C11","key":"10.1016\/j.cpc.2026.110098_bib0002","doi-asserted-by":"crossref","first-page":"11803","DOI":"10.1029\/JC092iC11p11803","article-title":"A new numerical method for surface hydrodynamics","volume":"92","author":"West","year":"1987","journal-title":"J. Geophys. Res.: Oceans"},{"key":"10.1016\/j.cpc.2026.110098_bib0003","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.cpc.2016.02.017","article-title":"Hos-ocean: Open-source solver for nonlinear waves in open ocean based on high-Order spectral method","volume":"203","author":"Ducrozet","year":"2016","journal-title":"Comput. Phys. Commun."},{"issue":"1","key":"10.1016\/j.cpc.2026.110098_bib0004","doi-asserted-by":"crossref","first-page":"20","DOI":"10.26748\/KSOE.2022.034","article-title":"A study on the high-order spectral model capability to simulate a fully developed nonlinear sea states","volume":"37","author":"Kim","year":"2023","journal-title":"J. Ocean Eng. Technol."},{"issue":"10","key":"10.1016\/j.cpc.2026.110098_bib0005","doi-asserted-by":"crossref","DOI":"10.1063\/5.0229953","article-title":"Effects of nonlinearity on the crest shape of extreme irregular sea waves: nonlinear harmonic separation and analysis","volume":"36","author":"Spiliotopoulos","year":"2024","journal-title":"Phys. Fluids"},{"key":"10.1016\/j.cpc.2026.110098_bib0006","doi-asserted-by":"crossref","DOI":"10.1016\/j.oceaneng.2021.108715","article-title":"Modelling rogue waves in 1d wave trains with the jonswap spectrum, by means of the high order spectral method and a fully nonlinear numerical model","volume":"231","author":"Kirezci","year":"2021","journal-title":"Ocean Eng."},{"key":"10.1016\/j.cpc.2026.110098_bib0007","doi-asserted-by":"crossref","DOI":"10.1016\/j.oceaneng.2022.111901","article-title":"A GPU-accelerated domain decomposition method for numerical analysis of nonlinear waves-current-structure interactions","volume":"259","author":"Lu","year":"2022","journal-title":"Ocean Eng."},{"issue":"11","key":"10.1016\/j.cpc.2026.110098_bib0008","doi-asserted-by":"crossref","DOI":"10.1063\/5.0070246","article-title":"Reduced order model for nonlinear multi-directional ocean wave propagation","volume":"33","author":"Bukka","year":"2021","journal-title":"Phys. Fluids"},{"key":"10.1016\/j.cpc.2026.110098_bib0009","doi-asserted-by":"crossref","DOI":"10.1017\/jfm.2023.841","article-title":"Nonlinear deterministic reconstruction and prediction of remotely measured ocean surface waves","volume":"975","author":"Desmars","year":"2023","journal-title":"J. Fluid Mech."},{"issue":"2","key":"10.1016\/j.cpc.2026.110098_bib0010","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1007\/BF00913182","article-title":"Stability of periodic waves of finite amplitude on the surface of a deep fluid","volume":"9","author":"Zakharov","year":"1968","journal-title":"J. Appl. Mech. Tech. Phys."},{"issue":"3","key":"10.1016\/j.cpc.2026.110098_bib0011","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1145\/79505.79507","article-title":"A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides","volume":"16","author":"Karp","year":"1990","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"issue":"2","key":"10.1016\/j.cpc.2026.110098_bib0012","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1016\/j.jcp.2004.11.027","article-title":"An efficient model for three-dimensional surface wave simulations: Part i: Free space problems","volume":"205","author":"Fructus","year":"2005","journal-title":"J. Comput. Phys."},{"issue":"11","key":"10.1016\/j.cpc.2026.110098_bib0013","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.1002\/fld.2672","article-title":"A comparative study of two fast nonlinear free-surface water wave models","volume":"69","author":"Ducrozet","year":"2012","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"10.1016\/j.cpc.2026.110098_bib0014","series-title":"Advances in Numerical Simulation of Nonlinear Water Waves","first-page":"129","article-title":"Time domain simulation of nonlinear water waves using spectral methods","author":"Bonnefoy","year":"2010"},{"key":"10.1016\/j.cpc.2026.110098_bib0015","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.oceaneng.2017.07.003","article-title":"Applicability and limitations of highly non-linear potential flow solvers in the context of water waves","volume":"142","author":"Ducrozet","year":"2017","journal-title":"Ocean Eng."},{"issue":"1","key":"10.1016\/j.cpc.2026.110098_bib0016","doi-asserted-by":"crossref","first-page":"109","DOI":"10.5194\/nhess-7-109-2007","article-title":"3-D HOS Simulations of extreme waves in open seas","volume":"7","author":"Ducrozet","year":"2007","journal-title":"Nat. Hazards Earth Syst. Sci."},{"issue":"2","key":"10.1016\/j.cpc.2026.110098_bib0017","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1109\/JPROC.2004.840301","article-title":"The design and implementation of FFTW3","volume":"93","author":"Frigo","year":"2005","journal-title":"Proc. IEEE"},{"key":"10.1016\/j.cpc.2026.110098_bib0018","series-title":"Proc. 18Th Int. Symp. on Offshore and Polar Engng.","article-title":"Analysis of freak waves formation with large scale fully nonlinear high order spectral simulations","author":"Ducrozet","year":"2008"},{"issue":"1","key":"10.1016\/j.cpc.2026.110098_bib0019","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.jcp.2005.04.008","article-title":"Modeling extreme waves based on equations of potential flow with a free surface","volume":"210","author":"Chalikov","year":"2005","journal-title":"J. Comput. Phys."},{"issue":"2","key":"10.1016\/j.cpc.2026.110098_bib0020","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/s42286-019-00014-9","article-title":"Account of occasional wave breaking in numerical simulations of irregular water waves in the focus of the rogue wave problem","volume":"2","author":"Slunyaev","year":"2020","journal-title":"Water Waves"},{"key":"10.1016\/j.cpc.2026.110098_bib0021","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1017\/jfm.2013.37","article-title":"Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution","volume":"720","author":"Xiao","year":"2013","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.cpc.2026.110098_bib0022","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.ocemod.2017.09.006","article-title":"Simulation of breaking waves using the high-order spectral method with laboratory experiments: Wave-breaking onset","volume":"119","author":"Seiffert","year":"2017","journal-title":"Ocean Modell."},{"issue":"1","key":"10.1016\/j.cpc.2026.110098_bib0023","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s10236-017-1119-3","article-title":"Simulation of breaking waves using the high-order spectral method with laboratory experiments: wave-breaking energy dissipation","volume":"68","author":"Seiffert","year":"2018","journal-title":"Ocean Dyn."},{"key":"10.1016\/j.cpc.2026.110098_bib0024","series-title":"ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering","article-title":"A comparative study of wave breaking models in a high-order spectral model","author":"Seiffert","year":"2017"},{"key":"10.1016\/j.cpc.2026.110098_bib0025","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1017\/jfm.2018.93","article-title":"On a unified breaking onset threshold for gravity waves in deep and intermediate depth water","volume":"841","author":"Barthelemy","year":"2018","journal-title":"J. Fluid Mech."},{"issue":"7","key":"10.1016\/j.cpc.2026.110098_bib0026","doi-asserted-by":"crossref","DOI":"10.1029\/2019JC015886","article-title":"A unified breaking onset criterion for surface gravity water waves in arbitrary depth","volume":"125","author":"Derakhti","year":"2020","journal-title":"J. Geophys. Res.: Oceans"},{"key":"10.1016\/j.cpc.2026.110098_bib0027","doi-asserted-by":"crossref","DOI":"10.1016\/j.coastaleng.2023.104316","article-title":"Unified depth-limited wave breaking detection and dissipation in fully nonlinear potential flow models","volume":"183","author":"Mohanlal","year":"2023","journal-title":"Coastal Eng."},{"key":"10.1016\/j.cpc.2026.110098_bib0028","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.coastaleng.2014.08.002","article-title":"High order Hamiltonian water wave models with wave-breaking mechanism","volume":"93","author":"Kurnia","year":"2014","journal-title":"Coastal Eng."},{"key":"10.1016\/j.cpc.2026.110098_bib0029","series-title":"39Th International Workshop on Water Waves and Floating Bodies","article-title":"Evaluating instantaneous crest phase speed in multi-directional seas through hilbert transform","author":"Wang","year":"2024"},{"key":"10.1016\/j.cpc.2026.110098_bib0030","doi-asserted-by":"crossref","DOI":"10.1016\/j.oceaneng.2025.121357","article-title":"Computing local crest phase speed in multi-directional sea states through the Spatial Hilbert Transform","volume":"331","author":"Wang","year":"2025","journal-title":"Ocean Engineering"},{"key":"10.1016\/j.cpc.2026.110098_bib0031","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1017\/S0022112010000832","article-title":"Energy dissipation in two-dimensional unsteady plunging breakers and an eddy viscosity model","volume":"655","author":"Tian","year":"2010","journal-title":"J. Fluid Mech."},{"issue":"3","key":"10.1016\/j.cpc.2026.110098_bib0032","doi-asserted-by":"crossref","DOI":"10.1063\/1.3687508","article-title":"An eddy viscosity model for two-dimensional breaking waves and its validation with laboratory experiments","volume":"24","author":"Tian","year":"2012","journal-title":"Phys. Fluids"},{"key":"10.1016\/j.cpc.2026.110098_bib0033","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.euromechflu.2012.01.017","article-title":"A modified high-order spectral method for wavemaker modeling in a numerical wave tank","volume":"34","author":"Ducrozet","year":"2012","journal-title":"Eur. J. Mech.-B\/Fluids"},{"key":"10.1016\/j.cpc.2026.110098_bib0034","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.euromechflu.2015.12.004","article-title":"Development and validation of a non-linear spectral model for water waves over variable depth","volume":"57","author":"Gouin","year":"2016","journal-title":"Eur. J. Mech.-B\/Fluids"},{"key":"10.1016\/j.cpc.2026.110098_bib0035","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.euromechflu.2017.01.002","article-title":"Propagation of 3D nonlinear waves over an elliptical mound with a high-order spectral method","volume":"63","author":"Gouin","year":"2017","journal-title":"Eur. J. Mech.-B\/Fluids"},{"key":"10.1016\/j.cpc.2026.110098_bib0036","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1017\/S0022112097007969","article-title":"On generalized Bragg scattering of surface waves by bottom ripples","volume":"356","author":"Liu","year":"1998","journal-title":"J. Fluid Mech."},{"issue":"2055","key":"10.1016\/j.cpc.2026.110098_bib0037","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1098\/rspa.2004.1367","article-title":"Hamiltonian long\u2013wave expansions for water waves over a rough bottom","volume":"461","author":"Craig","year":"2005","journal-title":"Proc. R. Soc. A: Math. Phys. Eng. Sci."},{"issue":"1","key":"10.1016\/j.cpc.2026.110098_bib0038","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1137\/060666214","article-title":"A high-order spectral method for nonlinear water waves over moving bottom topography","volume":"30","author":"Guyenne","year":"2008","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cpc.2026.110098_bib0039","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s40722-017-0086-6","article-title":"Influence of varying bathymetry in rogue wave occurrence within unidirectional and directional sea-states","volume":"3","author":"Ducrozet","year":"2017","journal-title":"J. Ocean Eng. Mar. Energy"},{"key":"10.1016\/j.cpc.2026.110098_bib0040","article-title":"Kinematics of waves breaking partially on an offshore bar; LDV measurements of waves with and without a net onshore current","volume":"40","author":"Luth","year":"1994","journal-title":"Report H-1573, Delft Hydraulics"},{"key":"10.1016\/j.cpc.2026.110098_bib0041","series-title":"Direct simulation and deterministic prediction of large-scale nonlinear ocean wave-field","author":"Wu","year":"2004"},{"key":"10.1016\/j.cpc.2026.110098_bib0042","series-title":"Theory and applications of ocean surface waves: Part 1: linear aspects","author":"Mei","year":"2005"},{"issue":"6","key":"10.1016\/j.cpc.2026.110098_bib0043","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevFluids.6.064803","article-title":"Predicting the occurrence of rogue waves in the presence of opposing currents with a high-order spectral method","volume":"6","author":"Ducrozet","year":"2021","journal-title":"Phys. Rev. Fluids"},{"key":"10.1016\/j.cpc.2026.110098_bib0044","unstructured":"HOS-Ocean Online Documentation, (https:\/\/lheea.gitlab.io\/HOS-Ocean). Accessed: 2025-09-11."},{"issue":"1","key":"10.1016\/j.cpc.2026.110098_bib0045","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/S0169-5983(00)00011-3","article-title":"A method of studying nonlinear random field of surface gravity waves by direct numerical simulation","volume":"28","author":"Tanaka","year":"2001","journal-title":"Fluid Dyn. Res."},{"key":"10.1016\/j.cpc.2026.110098_bib0046","unstructured":"Y. Choi, M. Gouin, G. Ducrozet, B. Bouscasse, P. Ferrant, Grid2Grid: HOS wrapper program for CFD solvers, arXiv: 1801.00026(2017)."},{"key":"10.1016\/j.cpc.2026.110098_bib0047","article-title":"An efficient methodology for the simulation of nonlinear irregular waves in computational fluid dynamics solvers based on the high order spectral method with an application with OpenFOAM","volume":"15","author":"Choi","year":"2023","journal-title":"Int. J. Naval Archi. Ocean Eng."},{"key":"10.1016\/j.cpc.2026.110098_bib0048","series-title":"International Conference on Offshore Mechanics and Arctic Engineering","article-title":"The generation of nonlinear short-Crested ocean waves from high order spectral method in a computational fluid dynamics solver","volume":"88926","author":"Tierno","year":"2025"},{"key":"10.1016\/j.cpc.2026.110098_bib0049","doi-asserted-by":"crossref","DOI":"10.1016\/j.oceaneng.2022.112206","article-title":"Numerical coupling strategy using HOS-OpenFOAM-MoorDyn for OC3 Hywind SPAR type platform","volume":"263","author":"Aliyar","year":"2022","journal-title":"Ocean Eng."},{"issue":"2","key":"10.1016\/j.cpc.2026.110098_bib0050","doi-asserted-by":"crossref","first-page":"227","DOI":"10.3390\/jmse12020227","article-title":"High-Order spectral irregular wave generation procedure in experimental and computational fluid dynamics numerical wave tanks, with application in a physical wave tank and in open-Source field operation and manipulation","volume":"12","author":"Kim","year":"2024","journal-title":"J. Mar. Sci. Eng."}],"container-title":["Computer Physics Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010465526000809?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010465526000809?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:05:28Z","timestamp":1777421128000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0010465526000809"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":50,"alternative-id":["S0010465526000809"],"URL":"https:\/\/doi.org\/10.1016\/j.cpc.2026.110098","relation":{},"ISSN":["0010-4655"],"issn-type":[{"value":"0010-4655","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"HOS-Ocean v2.1: Extensions of a nonlinear wave solver based on the High-Order Spectral method","name":"articletitle","label":"Article Title"},{"value":"Computer Physics Communications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cpc.2026.110098","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"110098"}}