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Preliminary Concepts
Published in Hillel Rubin, Joseph Atkinson, Environmental Fluid Mechanics, 2001
The concept of the kinematic wave is associated with estimates of phenomena connected with flood wave propagation in rivers and channels. A flood wave is a positive wave, namely, a rise of the water depth that propagates downstream. Since the rise of the water depth is only moderate, it is possible to consider that the channel bed slope and the friction slope of the channel flow are almost identical, and effects of friction on the wave propagation cannot be neglected. Therefore the channel discharge, Q, is solely a function of the water depth, y, and the features of the propagating wave are determined only by the equation of mass conservation. From Eq. (8.7.3), this is written as
Hydraulic Methods for Unsteady Flows
Published in James L. Martin, Steven C. McCutcheon, Robert W. Schottman, Hydrodynamics and Transport for Water Quality Modeling, 2018
James L. Martin, Steven C. McCutcheon, Robert W. Schottman
Numerical solutions to the kinematic-wave model area available in a number of hydraulic and water quality models, often as one of a selection of routing methods. For example, the kinematic-wave model is an optional routing method in the widely used flood hydrograph model HEC-1 (HEC 1980) and the scheme illustrated above is one of the solution schemes used in that model. The WQRRS river or reservoir model (HEC 1978) solves the kinematic-wave model using a finite-element technique. Other available models solve the kinematic-wave model using finite-element or finite-difference schemes, both explicit and implicit.
Modelling of open-channel systems
Published in P. Novak, V. Guinot, A. Jeffrey, D.E. Reeve, Hydraulic Modelling – an Introduction, 2010
P. Novak, V. Guinot, A. Jeffrey, D.E. Reeve
The kinematic wave approximation results from a further simplification of the diffusive wave approximation. It is suitable for the simulation of shallow-water flows over steep slopes, where the slope of the energy line becomes equivalent to that of the channel bottom and where inertial effects can be neglected because the flow velocity remains reasonably small. The solution of the kinematic wave equation is made of a single wave travelling downstream at a speed different from that of the flow (Figure 7.8(c)). As there is only one wave, travelling in a single direction, the kinematic wave approximation does not allow backwater effects to be accounted for.
A macroscopic flow model for mixed bicycle–car traffic
Published in Transportmetrica A: Transport Science, 2021
M. J. Wierbos, V. L. Knoop, F. S. Hänseler, S. P. Hoogendoorn
Although the Eulerian method is most commonly used, the Lagrangian method has been successfully applied to numerically solve the kinematic wave model as well. This has been done for homogeneous traffic (Leclercq 2007; Wu et al. 2014), as well as mixed traffic including trucks (van Wageningen-Kessels et al. 2011) and motor cyclists (Gashaw, Harri, and Goatin 2018). Examples of the Lagrangian method applied to second-order flow models are Greenberg (2001, 2004); Zhang, Wu, and Wong (2012). In the macroscopic approach, the Lagrangian method calculates the traffic evolution for platoons consisting of multiple vehicles, whereas the microscopic approach gives the trajectories of individual traffic participants. The macroscopic model reduces to a microscopic car-following model when the platoon size is reduced to one vehicle only, as shown e.g. by (Aw et al. 2002) and Leclercq (2007). Information travels downstream only in the Lagrangian Godunov scheme, making it less prone for errors due to numerical diffusion. Using the Lagrangian methods therefore results in a more robust model compared to the Eulerian scheme where information travels both up and downstream.