scholarly journals Estimation of uncertainty in an open-channel network mathematical model

1989 ◽  
Vol 13 (11) ◽  
pp. 651-657 ◽  
Author(s):  
G. Corriga ◽  
S. Sanna ◽  
G. Usai
Keyword(s):  
Mathematical Model ◽  
Open Channel ◽  
Channel Network ◽  
Estimation Of Uncertainty

scholarly journals Automated Detection of Instability-Inducing Channel Geometry Transitions in Saint-Venant Simulation of Large-Scale River Networks

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2236
Author(s):  
Cheng-Wei Yu ◽  
Ben R. Hodges ◽  
Frank Liu
Keyword(s):  
Large Scale ◽  
Open Channel ◽  
Search Algorithm ◽  
Shallow Water Equation ◽  
Stable Solution ◽  
River Networks ◽  
River Systems ◽  
Channel Network ◽  
Channel Geometry ◽  
Venant Equation

A new sweep-search algorithm (SSA) is developed and tested to identify the channel geometry transitions responsible for numerical convergence failure in a Saint-Venant equation (SVE) simulation of a large-scale open-channel network. Numerical instabilities are known to occur at “sharp” transitions in discrete geometry, but the identification of problem locations has been a matter of modeler’s art and a roadblock to implementing large-scale SVE simulations. The new method implements techniques from graph theory applied to a steady-state 1D shallow-water equation solver to recursively examine the numerical stability of each flowpath through the channel network. The SSA is validated with a short river reach and tested by the simulation of ten complete river systems of the Texas–Gulf Coast region by using the extreme hydrological conditions recorded during hurricane Harvey. The SSA successfully identified the problematic channel sections in all tested river systems. Subsequent modification of the problem sections allowed stable solution by an unsteady SVE numerical solver. The new SSA approach permits automated and consistent identification of problem channel geometry in large open-channel network data sets, which is necessary to effectively apply the fully dynamic Saint-Venant equations to large-scale river networks or for city-wide stormwater networks.

scholarly journals Mathematical Modeling of Pollution Transfer in Open Channel

2019 ◽  
pp. 49-50
Author(s):  
Petro Martyniuk ◽  
Oksana Ostapchuk ◽  
Vitalii Nalyvaiko
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Solution ◽  
Boundary Problem ◽  
Water Flow ◽  
Numerical Experiments ◽  
Open Channel ◽  
Computational Algorithm ◽  
The Mathematical Model

The problem of pollution transfer by water flow in open channel was considered. The mathematical model of the problem was constructed. The numerical solution of the onedimensional boundary problem was obtained. The computational algorithm for solving the problem was programmed to implement. A series of numerical experiments with their further analysis was conducted.

Implicit Bidiagonal Numerical Scheme for Simulation of 2D Flood Waves

2011 ◽  
Vol 356-360 ◽  
pp. 2293-2296
Author(s):  
Guang Cai Sun
Keyword(s):  
Mathematical Model ◽  
Numerical Scheme ◽  
Open Channel ◽  
Water Velocity ◽  
Dam Break ◽  
Rectangular Cylinder ◽  
Predictor Corrector ◽  
The Mathematical Model ◽  
Depth Water ◽  
Flood Waves

This paper is concerned with a mathematical model for numerical simulation of 2D flood waves due to partial dam-break. The governing water equations are solved by an implicit bidiagonal numerical scheme, based on the MacCormack’s predictor-corrector technique. The mathematical model is used to compute 2D flood waves due to partial instantaneous symmetrical dam-break in a rectangular open channel with a rectangular cylinder barrier downstream. Results, in terms of water velocity vectors and contours of water depth, water surface, following dam-break phenomena, are investigated in the two-dimensional problems.

A mathematical model for long waves generated by wavemakers in non-linear dispersive systems

1973 ◽  
Vol 73 (2) ◽  
pp. 391-405 ◽  
Author(s):  
J. L. Bona ◽  
P. J. Bryant
Keyword(s):  
Mathematical Model ◽  
Initial Data ◽  
Water Waves ◽  
Open Channel ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Finite Amplitude ◽  
Mathematical Properties ◽  
Image Position ◽  
Initial Boundary Value

An initial-boundary-value problem for the equationis considered for x, t ≥ 0. This system is a model for long water waves of small but finite amplitude, generated in a uniform open channel by a wavemaker at one end. It is shown that, in contrast to an alternative, more familiar model using the Korteweg–deVries equation, the solution of (a) has good mathematical properties: in particular, the problem is well set in Hadamard's classical sense that solutions corresponding to given initial data exist, are unique, and depend continuously on the specified data.

Numerical Simulation of Hydraulic Jump

2011 ◽  
Vol 374-377 ◽  
pp. 643-646
Author(s):  
Ming Qin Liu ◽  
Yu Ling Liu
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Hydraulic Jump ◽  
Open Channel ◽  
2D Flow ◽  
Predictor Corrector ◽  
The Mathematical Model

This paper is concerned with a mathematical model for numerical simulation of 2D flow accompanied with a hydraulic jump. The governing water equations are solved by the MacCormack’s predictor-corrector technique. The mathematical model is used to numerically predict 2D hydraulic jump in a rectangular open channel. The comparison and the analysis show that the proposed method is accurate, reliable and effective in simulation of hydraulic jump flows.

scholarly journals Optimization of water distribution for open-channel irrigation networks

2013 ◽  
Vol 16 (2) ◽  
pp. 341-353 ◽  
Author(s):  
Sothea Hong ◽  
Pierre-Olivier Malaterre ◽  
Gilles Belaud ◽  
Cyril Dejean
Keyword(s):  
Water Distribution ◽  
Open Channel ◽  
Optimization Approach ◽  
Start Time ◽  
Time Duration ◽  
Channel Network ◽  
Water Losses ◽  
Numerical Resolution ◽  
Irrigation Networks ◽  
Demand Patterns

Water distribution for open-channel irrigation networks is more and more complex due to increasing constraints on water resources and changing demand patterns, whereas the performance of such systems is expected to increase. In this regard, an optimization approach is developed in order to schedule a fair scenario of water distribution among different users, where water demand is formulated in term of start time, duration and flow rate. This study investigates how to optimize the water distribution over a finite scheduling horizon while respecting the constraints linked to the system. The optimization approach forces the scheduled start time and the volume to be closer to the demanded ones, to minimize water losses and to reduce manpower. The constraints take into account the flow routing processes, the physical infrastructure, the available water resource, and the gate keeper timetable. The numerical resolution is done by using an optimization software IBM-Ilog Cplex. The method is then illustrated with the scheduling of off-take withdrawals for a typical traditional open-channel network: a lateral canal of the Gignac canal, in southern France.

A depth-averaged mathematical model for the near field of side discharges into open-channel flow

1978 ◽  
Vol 86 (4) ◽  
pp. 761-781 ◽  
Author(s):  
J. J. Mcguirk ◽  
W. Rodi
Keyword(s):  
Mathematical Model ◽  
Channel Flow ◽  
Open Channel ◽  
Recirculation Zone ◽  
Essential Feature ◽  
Near Field ◽  
Open Channel Flow ◽  
Wide Range ◽  
Channel Velocity ◽  
Source Sink

A two-dimensional mathematical model is described for the calculation of the depth-averaged velocity and temperature or concentration distribution in open-channel flows, an essential feature of the model being its ability to handle recirculation zones. The model employs the depth-averaged continuity, momentum and temperature/concentration equations, which are solved by an efficient finite-difference procedure. The ‘rigid lid’ approximation is used to treat the free surface. The turbulent stresses and heat or concentration fluxes are determined from a depth-averaged version of the so-calledk, ε turbulence model which characterizes the local state of turbulence by the turbulence kinetic energykand the rate of its dissipation ε. Differential transport equations are solved forkand ε to determine these two quantities. The bottom shear stress and turbulence production are accounted for by source/sink terms in the relevant equations. The model is applied to the problem of a side discharge into open-channel flow, where a recirculation zone develops downstream of the discharge. Predicted size of the recirculation zone, jet trajectories, dilution, and isotherms are compared with experiments for a wide range of discharge to channel velocity ratios; the agreement is generally good. An assessment of the numerical accuracy shows that the predictions are not influenced significantly by numerical diffusion.

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