Shallow water equations applied to dam break analysis

Authors

DOI:

https://doi.org/10.5902/2179460X90599

Keywords:

Shallow waters, Finite elements, Dam break, Numerical methods, Mathematical modeling

Abstract

This work presents the shallow water equation, which takes into account variations in quantities (water height and flow speed). This equation will be used to model dam failure problems in areas where the variation in the lateral direction (y) is significant, such as in valleys or uneven terrain. Since this is a simplification of the Navier-Stokes equations, it is assumed that the depth variation in the vertical (z) direction is much smaller compared to the horizontal dimensions of the problem. For the numerical solution of this equation, the finite element method is used in the semi-implicit form of the general formulation of the characteristic variables. A case study will be addressed, showing validation with results from the literature.

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Author Biographies

Gustavo Braz Kurz, Universidade Federal de Pelotas

Graduated in Mathematics (2021) from the Federal University of Pelotas (UFPEL). Currently studying in the postgraduate program in Mathematical Modeling at UFPEL, in the area of ​​computational fluid dynamics, working with the shallow water equation. Solving these equations through finite elements spatially and in time using the CBS (Characteristic-Based-Split) method.

Renato Vaz Linn, Universidade Federal do Rio Grande do Sul

Civil Engineering (2010), Master (2013) and Doctor in Civil Engineering in the Structural Mechanics Area by Federal University of Rio Grande do Sul (UFRGS). 

Daniela Buske, Universidade Federal de Pelotas

He has a degree in Mathematics Full Degree from the Federal University of Santa Maria (1999), a master's and doctorate in Mechanical Engineering from the Federal University of Rio Grande do Sul (2004;2008) in the area of ​​Transport Phenomena / Pollutant Dispersion and a post-doctorate from Federal University of Rio Grande do Sul (2011) in the area of ​​Nuclear Engineering. 

Leonidas Alejandro Arias Baltazar, Universidade Federal de Lavras

He holds a PhD in Water Resources, Area of ​​Concentration in Water Resources, from the Federal University of Lavras (2023), and is a PhD candidate in Applied Meteorology from the Federal University of Viçosa (2023). He has a Master's degree in Hydrological and Hydraulic Engineering from the Technical University of Oruro (2017), and a degree in Agricultural Engineering from the National Agricultural University La Molina, Lima-Peru (1990). 

Régis Sperotto Quadros, Universidade Federal de Pelotas

He holds a degree in Mathematics from the University of Passo Fundo (2000), a master's degree in Applied Mathematics from the Federal University of Rio Grande do Sul (2003), a PhD in Applied Mathematics from the Technische Universität Darmstadt in Darmstadt, Germany (2009), and a postdoctoral degree in Nuclear Energy from the Federal University of Rio Grande do Sul (2014).

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Published

2025-02-14

How to Cite

Kurz, G. B., Linn, R. V., Buske, D., Baltazar, L. A. A., & Quadros, R. S. (2025). Shallow water equations applied to dam break analysis. Ciência E Natura, 47(esp. 1). https://doi.org/10.5902/2179460X90599

Issue

Vol. 47 No. esp. 1 (2025): IV Jornada de Matematica e Matematica aplicada UFSM

Section

IV Jornada de Matematica e Matematica aplicada UFSM

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