The Cunge–Muskingum method

Let us talk about flood routing. The Muskingum flood routing method is an empirical stage-discharge relation developed in the 1930s, for flood control schemes in the Muskingum River catchment (USA). In this method, the river reach volume is linked to the inflow volume discharge and outflow discharge using empirical routing parameters of river reach. While the Muskingum flood routing method has been in use for decades, it is not until the 1960s that the 'apparent' success of the method was explained theoretically by Dr Jean Cunge: i.e., the Cunge-Muskingum method (Cunge 1969). The Cunge-Muskingum method is an application of the diffusive wave equation, which itself is a simplification of the Saint Venant equations (SVE) (Chanson 2004). There, the dynamic equation is simplified by neglecting the acceleration and inertia terms. After some re-arrangement (Chanson 2004, pp. 341-344), the combination of the equation of conservation of mass and of momentum (i.e. diffusive wave equation) yields a diffusion equation in terms of the volume discharge Q. Dr Jean Cunge showed that Muskingum flood routing method approaches a diffusion wave problem, i.e. the Cunge-Muskingum method, when the flood wave celerity and diffusion coefficient fulfill theoretical solutions. Acknowledgements Dr Jean CUNGE (1934-2023) - who was Prof. Chanson's lecturer in unsteady open channel flow; Professor Colin APELT; Professor Philippe GOURBESVILLE. References CUNGE, J.A. (1969). "On the Subject of a Flood Propagation Computation Method (Muskingum Method)." Journal of Hydraulic Research, IAHR, Vol. 7, No. 2, pp. 205-230. HENDERSON, F.M. (1966). "Open Channel Flow." MacMillan Company, New York, USA. LIGGETT, J.A. (1975). "Basic Equations of Unsteady Flow." in "Unsteady Flow in Open Channels." WRP Publ., Fort Collins, USA, K. MAHMOOD and V. YEVDJEVICH Ed., Vol. 1, pp. 29-62. MILLER, W.A., and CUNGE, J.A. (1975). "Simplified Equations of Unsteady Flows." in "Unsteady Flow in Open Channels." WRP Publ., Fort Collins, USA, K. MAHMOOD and V. YEVDJEVICH Ed., Vol. 1, pp. 183-257. CUNGE, J.A., HOLLY Jr, F.M., and VERWEY, A. (1980). "Practical Aspects of Computational River Hydraulics." Pitman, Boston, USA, 420 pages. CHANSON, H. (2004). "The Hydraulics of Open Channel Flow: An Introduction." Butterworth-Heinemann, 2nd edition, Oxford, UK, 630 pages (ISBN 978 0 7506 5978 9). CHANSON, H. (2004). "Environmental Hydraulics of Open Channel Flows." Elsevier-Butterworth-Heinemann, Oxford, UK, 483 pages (ISBN 978 0 7506 6165 2). Fluid mechanics and hydraulics in Hubert Chanson Youtube channel {https://www.youtube.com/@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 {https://www.youtube.com/watch?v=Q7FKefVaQ2k} Saint-Venant equations. (2) Basic equations {https://www.youtube.com/watch?v=RuLr_l8fXnY} Saint-Venant equations. (3) The continuity equation {https://www.youtube.com/watch?v=b-9kn9INsFw} Saint-Venant equations. (4) The dynamic equation {https://www.youtube.com/watch?v=JMEpharHV4k} Saint-Venant equations. (5) Simplification of the dynamic equation {https://www.youtube.com/watch?v=aeYwKk0Iy7M} Saint‐Venant equations & the simplification of the dynamic equation {https://www.youtube.com/watch?v=y9TC5i9mXYQ} The diffusive wave equation - Unsteady open channel flows and flood modelling {https://www.youtube.com/watch?v=p_mSo3el9RE}