Numerical simulation of dam-break flow using a modified Runge-Kutta scheme with validation

Touazi, Lamia (author), Ikni, Tahar (author), Berreksi, Ali (author)

This paper presents a numerical scheme based on the second-order Runge‒Kutta method, combined with finite-difference spatial discretisation, for simulating dam-break flows governed by the one-dimensional SaintVenant equations. The proposed method introduces a flow decomposition coupled with an artificial viscosity term inspired by previous work, in order to improve the numerical stability and accuracy of the results. A comparative analysis is carried out between the classical scheme and the modified Runge‒Kutta second-order scheme using an analytical solution as a reference. The results show that the modified scheme is significantly better matched to the analytical solution. The method is then applied to several dam failure scenarios including complex conditions such as triangular and trapezoidal obstacles, sloping bottoms and dry bed/wet bed transitions. The numerical results are compared with experimental data and simulation results published in the specialist literature. In all cases, the modified scheme performs better confirming its robustness and accuracy for modelling the propagation of dam burst waves under complex hydraulic conditions.

• Language: English
• Keywords: dam-break, Saint-Venant, modelling, Runge‒Kutta classical scheme, friction, Runge‒Kutta modified scheme
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 65-85
• Numbering: Vol. 38, no. 69
• PID: 20.500.12556/RUL-181288
• UDC: 519.6:627.82(078.7)
• ISSN on article: 0352-3551
• DOI: 10.15292/acta.hydro.2025.06
• COBISS.SI-ID: 273644547
• Publication date in RUL: 31.03.2026

Record is a part of a journal

• Title: Acta hydrotechnica
• Publisher: Fakulteta za gradbeništvo in geodezijo
• ISSN: 0352-3551
• COBISS.SI-ID: 3664386

Licences

• License: CC BY-SA 4.0, Creative Commons Attribution-ShareAlike 4.0 International
• Link: http://creativecommons.org/licenses/by-sa/4.0/
• Description: This Creative Commons license is very similar to the regular Attribution license, but requires the release of all derivative works under this same license.

Secondary language

• Language: Slovenian
• Title: Numerična simulacija toka ob porušitvi pregrade z uporabo modificirane sheme Runge-Kutta z validacijo

Abstract

V članku je predstavljena numerična shema, ki temelji na metodi Runge‒Kutta drugega reda v kombinaciji s prostorsko diskretizacijo z metodo končnih razlik za simulacijo tokov ob porušitvi pregrade, ki jih opisujejo enodimenzionalne Saint-Venantove enačbe. Predlagana metoda uvaja razdelitev toka v kombinaciji z umetnim, viskoznim členom, ki temelji na prejšnjem delu, da bi se izboljšala numerična stabilnost in natančnost rezultatov. Izvedena je primerjalna analiza med klasično in modificirano shemo Runge‒Kutta drugega reda, pri čemer se kot referenca uporabi analitična rešitev. Rezultati kažejo, da se modificirana shema bistveno bolje ujema z analitično rešitvijo. Metoda se nato uporabi za več scenarijev porušitve pregrade, vključno z zahtevnimi pogoji, kot so trikotne in trapezne ovire, nagnjeno dno in prehodi med suhim in mokrim dnom. Numerični rezultati so primerjani z eksperimentalnimi podatki in rezultati simulacij, objavljenimi v strokovni literaturi. V vseh primerih se modificirana shema izkaže kot učinkovitejša, kar potrjuje njeno robustnost in natančnost pri modeliranju širjenja vala ob porušitvi pregrade v zahtevnih hidravličnih pogojih.

• Keywords: porušitev pregrade, Saint-Venant, modeliranje, klasična shema Runge‒Kutta, trenje, modificirana shema Runge‒Kutta