{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T17:19:42Z","timestamp":1769102382961,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T00:00:00Z","timestamp":1605484800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51779055"],"award-info":[{"award-number":["51779055"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JMSE"],"abstract":"<jats:p>The hydrodynamic interaction induced by the complex flow around a ship maneuvering in restricted waters has a significant influence on navigation safety. In particular, when a ship moves in the vicinity of a bank, the hydrodynamic interaction forces caused by the bank effect can significantly affect the ship\u2019s maneuverability. An efficient algorithm integrated in onboard systems or simulators for capturing the bank effect with fair accuracy would benefit navigation safety. In this study, an algorithm based on the potential-flow theory is presented for efficient calculation of ship-bank hydrodynamic interaction forces. Under the low Froude number assumption, the free surface boundary condition is approximated using the double-body model. A layer of sources is dynamically distributed on part of the seabed and bank in the vicinity of the ship to model the boundary conditions. The sinkage and trim are iteratively solved via hydrostatic balance, and the importance of including sinkage and trim is investigated. To validate the numerical method, a series of simulations with various configurations are carried out, and the results are compared with experiment and numerical results obtained with RANSE-based and Rankine source methods. The comparison and analysis show the accuracy of the method proposed in this paper satisfactory except for extreme shallow water cases.<\/jats:p>","DOI":"10.3390\/jmse8110927","type":"journal-article","created":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T21:48:52Z","timestamp":1605563332000},"page":"927","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Fast Algorithm for the Prediction of Ship-Bank Interaction in Shallow Water"],"prefix":"10.3390","volume":"8","author":[{"given":"Jin","family":"Huang","sequence":"first","affiliation":[{"name":"College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"International Joint Laboratory of Naval Architecture and Offshore Technology between Harbin Engineering University and Lisbon University, Harbin 150001, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-2665-220X","authenticated-orcid":false,"given":"Chen","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"International Joint Laboratory of Naval Architecture and Offshore Technology between Harbin Engineering University and Lisbon University, Harbin 150001, China"}]},{"given":"Ping","family":"Xin","sequence":"additional","affiliation":[{"name":"College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"International Joint Laboratory of Naval Architecture and Offshore Technology between Harbin Engineering University and Lisbon University, Harbin 150001, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1583-414X","authenticated-orcid":false,"given":"Xueqian","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"International Joint Laboratory of Naval Architecture and Offshore Technology between Harbin Engineering University and Lisbon University, Harbin 150001, China"}]},{"given":"Serge","family":"Sutulo","sequence":"additional","affiliation":[{"name":"International Joint Laboratory of Naval Architecture and Offshore Technology between Harbin Engineering University and Lisbon University, Harbin 150001, China"},{"name":"Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8570-4263","authenticated-orcid":false,"given":"Carlos","family":"Guedes Soares","sequence":"additional","affiliation":[{"name":"International Joint Laboratory of Naval Architecture and Offshore Technology between Harbin Engineering University and Lisbon University, Harbin 150001, China"},{"name":"Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"04020032","DOI":"10.1061\/(ASCE)WW.1943-5460.0000594","article-title":"Maneuverability-based approach for ship-bank collision probability under strong wind and ship-bank interaction","volume":"146","author":"Liu","year":"2020","journal-title":"J. Waterw. Port Coast. Ocean Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"S305","DOI":"10.1080\/17445302.2016.1264354","article-title":"Ship-bank interaction of a VLCC ship model and related course-keeping control","volume":"12","author":"Liu","year":"2017","journal-title":"Ships Offshore Struc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"106149","DOI":"10.1016\/j.oceaneng.2019.106149","article-title":"Maneuvering hydrodynamic derivatives and course stability of a ship close to a bank","volume":"188","author":"Yasukawa","year":"2019","journal-title":"Ocean. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"199","DOI":"10.2478\/IJNAOE-2013-0090","article-title":"A study on ship automatic berthing with assistance of auxiliary devices","volume":"4","author":"Tran","year":"2012","journal-title":"Int. J. Nav. Arch. Ocean Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.ifacol.2019.12.289","article-title":"Implementation and evaluation of non-linear optimal feedback control for ship\u2019s automatic berthing by recurrent neural network","volume":"52","author":"Mizuno","year":"2019","journal-title":"IFAC PapersOnLine"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1007\/s00773-012-0209-7","article-title":"Computational fluid dynamics (CFD) prediction of bank effects including verification and validation","volume":"18","author":"Zou","year":"2013","journal-title":"J. Mar. Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1080\/17445302.2016.1275475","article-title":"Bank effects on ship-ship hydrodynamic interaction in shallow water based on high-order panel method","volume":"12","author":"Xu","year":"2017","journal-title":"Ships Offshore Struc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1007\/s00773-018-0545-3","article-title":"Bank effects for KVLCC2","volume":"24","author":"Toxopeus","year":"2019","journal-title":"J. Mar. Sci. Technol."},{"key":"ref_9","unstructured":"Cooper, R.D., and Doroff, S.W. (1974, January 24\u201328). Bank effects on a ship moving through a short dredged channel. Proceedings of the 10th Symposium On Naval Hydrodynamics, Hydrodynamics For Safety, Fundamental Hydrodynamics, Cambridge, MA, USA."},{"key":"ref_10","unstructured":"Lataire, E., and Delefortrie, G. (2007, January 28\u201330). Navigation in confined waters: Influence of bank characteristics on ship-bank interaction. Proceedings of the 2nd International Conference on Marine Research and Transportation, Ischia & Naples, Italy."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Lataire, E., Vantorre, M., and Eloot, K. (2009, January 13\u201315). Systematic model tests on ship-bank interaction. Proceedings of the International Conference on Ship Manoeuvring in Shallow and Confined Water: Bank Effects, Antwerp, Belgium.","DOI":"10.3940\/rina.bank.2009.16"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"021304","DOI":"10.1115\/1.4038804","article-title":"The influence of the ship\u2019s speed and distance to an arbitrarly shaped bank on bank effects","volume":"140","author":"Lataire","year":"2017","journal-title":"J. Offshore Mech. Arct."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Sutulo, S., and Guedes Soares, C. (2008, January 15\u201319). Simulation of the hydrodynamic interaction forces in close-proximity manoeuvring. Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering (OMAE), Estoril, Portugal.","DOI":"10.1115\/OMAE2008-57938"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"107","DOI":"10.5957\/jsr.1977.21.2.107","article-title":"Forces and moments on a ship moving in a shallow channel","volume":"21","author":"Beck","year":"1977","journal-title":"J. Ship Res."},{"key":"ref_15","first-page":"22","article-title":"Prediction method for ship manoeuvring motion in the proximity of a pier","volume":"44","author":"Kijima","year":"1997","journal-title":"Ship Tech. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1016\/S1001-6058(13)60428-X","article-title":"Hydrodynamic interaction among hull, rudder and bank for a ship sailing along a bank in restricted waters","volume":"25","author":"Ma","year":"2013","journal-title":"J. Hydrodyn. Ser. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/S1001-6058(16)60727-8","article-title":"Numerical estimation of ship-propeller-hull interaction effect on ship manoeuvring using CFD method","volume":"29","author":"Kaidi","year":"2017","journal-title":"J. Hydrodyn. Ser. B"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"16","DOI":"10.5957\/JOSR.04170020","article-title":"Ship hydrodynamics in confined waterways","volume":"63","author":"Yuan","year":"2019","journal-title":"J. Ship Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"22","DOI":"10.5957\/jsr.1964.8.4.22","article-title":"Calculation of non-lifting potential flow about arbitrary three-dimensional bodies","volume":"8","author":"Hess","year":"1964","journal-title":"J. Ship Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"129","DOI":"10.5957\/jsr.2012.56.3.129","article-title":"Validation of potential-flow estimation of interaction forces acting upon ship hulls in parallel motion","volume":"56","author":"Sutulo","year":"2012","journal-title":"J. Ship Res."},{"key":"ref_21","first-page":"285","article-title":"Computation of ship-to-ship interaction forces by a 3D potential flow panel method in finite water depth","volume":"136","author":"Zhou","year":"2010","journal-title":"J. Offshore Mech. Arct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"251","DOI":"10.5957\/JOSR.10180089","article-title":"Free-surface effects on interaction of multiple ships moving at different speeds","volume":"63","author":"Yuan","year":"2019","journal-title":"J. Ship Res."},{"key":"ref_23","unstructured":"Fonfach, J.M.A., Sutulo, S., and Guedes Soares, C. (2011, January 18\u201320). Numerical study of ship-to-ship interaction forces on the basis of various flow models. Proceedings of the 2nd International Conference on Ship Manoeuvring in Shallow and Confined Water: Ship to Ship Interaction, Trondheim, Norway."},{"key":"ref_24","first-page":"21","article-title":"CFD analysis of ship-to-ship hydrodynamic interaction","volume":"17","author":"Sutulo","year":"2018","journal-title":"J. Mar. Sci. Tech."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.oceaneng.2012.07.009","article-title":"A prediction method for squat in restricted and unrestricted rectangular fairways","volume":"55","author":"Lataire","year":"2012","journal-title":"Ocean Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"102143","DOI":"10.1016\/j.apor.2020.102143","article-title":"Numerical investigation of scale effect in self-propelled container ship squat","volume":"99","author":"Kok","year":"2020","journal-title":"Appl. Ocean Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.oceaneng.2017.10.016","article-title":"Ship squat prediction using a potential flow rankine source method","volume":"148","author":"McTaggart","year":"2018","journal-title":"Ocean Eng."},{"key":"ref_28","first-page":"334","article-title":"Computational fluid dynamics prediction of hydrodynamic forces on a manoeuvring ship including effects of dynamic sinkage and trim","volume":"12","author":"Liu","year":"2017","journal-title":"Proc. Inst. Mech. Eng. Part M J. Eng. Marit. Environ."},{"key":"ref_29","unstructured":"Guedes Soares, C., and Santos, T.A. (2016). Study of ship-to-ship interaction in shallow water with account for squat phenomenon. Maritime Technology and Engineering 3, Taylor & Francis Group."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"051201","DOI":"10.1115\/1.4046484","article-title":"A numerical method for calculation of ship-ship hydrodynamics interaction in shallow water accounting for sinkage and trim","volume":"142","author":"Ren","year":"2020","journal-title":"J. Offshore Mech. Arct."},{"key":"ref_31","unstructured":"Lamb, H. (1945). Hydrodynamics, Dover Pub. [6th ed.]."},{"key":"ref_32","unstructured":"Japan P&I Club (2014). Preventing damage to harbour facilities and ship handling in Harbours, Part2. P&I Loss Prev. Bull., 32, 4\u20137."}],"container-title":["Journal of Marine Science and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2077-1312\/8\/11\/927\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:34:11Z","timestamp":1760178851000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2077-1312\/8\/11\/927"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,16]]},"references-count":32,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["jmse8110927"],"URL":"https:\/\/doi.org\/10.3390\/jmse8110927","relation":{},"ISSN":["2077-1312"],"issn-type":[{"value":"2077-1312","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,16]]}}}