Method of Characteristics in Open Channel Hydraulics. (4) Numerical integration incl. Hartree method скачать в хорошем качестве

Method of Characteristics in Open Channel Hydraulics. (4) Numerical integration incl. Hartree method

In an unsteady open channel flow, the Saint-Venant equations (SVE) are a system of two equations to solve one-dimensional unsteady flow motion, e.g. for flood modelling. One equation is the continuity equation, and the second one is the momentum equation. The method of characteristics is a technique for solving the differential form of the Saint-Venant equations, analytically, graphically and numerically. Herein, the numerical integration is discussed. A simple numerical integration of the characteristic system of equation is the Hartree method. The Hartree method uses fixed time and spatial intervals. The Hartree method is named after the English physicist Douglas R Hartree (1897-1958). The scheme is sometimes called the Hartree-Fock method after the Russian physicist V. Fock who generalised Hartree's scheme. The Saint-Venant equations and the characteristic system of equations are essential concepts for the numerical modelling of unsteady open channel flows and its practical applications, e.g. flood modelling. These are discussed in the relevant Youtube video movies in the same Playlist at: {   / @hubert_chanson  } Fluid mechanics and hydraulics in Hubert Chanson Youtube channel {   / @hubert_chanson  } Advanced hydraulics of open channel flows [Playlist] Fundamentals of open channel hydraulics [Playlist] Environmental hydraulics of open channel flows [Playlist] Saint-Venant equations. (1) Presentation {   • Saint-Venant equations. (1) Presentation  } Saint-Venant equations. (2) Basic equations {   • Saint-Venant equations. (2) Basic equations  } Saint-Venant equations. (3) The continuity equation {   • Saint-Venant equations. (3) The continuity...  } Saint-Venant equations. (4) The dynamic equation {   • Saint-Venant equations. (4) The dynamic eq...  } Saint-Venant equations. (5) Simplification of the dynamic equation {   • Saint-Venant equations. (5) Simplification...  } Method of Characteristics in Open Channel Hydraulics. (1) Presentation {   • Method of Characteristics in Open Channel ...  } Method of Characteristics in Open Channel Hydraulics. (2) Graphical solution {https://www.youtube.com/watch?v=1xcyK...} Method of Characteristics in Open Channel Hydraulics. (3) Boundary conditions {   • Method of Characteristics in Open Channel ...  } Celerity of small wave and its propagation in open channel {   • Celerity of small wave and its propagation...  } Courant number {   • Courant number  } Acknowledgements Dr Jean CUNGE Professor Colin APELT References STOKER, J.J. (1957). "Water Waves. The mathematical Theory with Applications." Interscience Publishers, New York, USA, 567 pages. MONTES, J.S. (1998). "Hydraulics of Open Channel Flow." ASCE Press, New-York, USA, 697 pages. CHANSON, H. (2004a). "The Hydraulics of Open Channel Flow: An Introduction." Butterworth-Heinemann, 2nd edition, Oxford, UK, 630 pages (ISBN 978 0 7506 5978 9). CHANSON, H. (2004b). "Environmental Hydraulics of Open Channel Flows." Elsevier-Butterworth-Heinemann, Oxford, UK, 483 pages (ISBN 978 0 7506 6165 2).