<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.</p></abstract>

In this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.

Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

Gdańsk University of Technology, Faculty of Civil and Environmental Engineering, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland

Archives of Hydro-Engineering and Environmental Mechanics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging...

Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

Published Online: Mar 17, 2016

Page range: 101 - 119

Received: Oct 09, 2015

DOI: https://doi.org/10.1515/heem-2015-0022

Keywords
standard step method, numerical integration, initial value problem, ordinary differential equation, open channel, steady gradually varied flow, energy slope

© 2015 Wojciech Artichowicz et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

Published Online: Mar 17, 2016

Page range: 101 - 119

Received: Oct 09, 2015

DOI: https://doi.org/10.1515/heem-2015-0022

Keywordsstandard step method, numerical integration, initial value problem, ordinary differential equation, open channel, steady gradually varied flow, energy slope

© 2015 Wojciech Artichowicz et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
standard step method, numerical integration, initial value problem, ordinary differential equation, open channel, steady gradually varied flow, energy slope