Special Issue "Shallow Water Equations in Hydraulics: Modeling, Numerics and Applications"

A special issue of Water (ISSN 2073-4441). This special issue belongs to the section "Hydraulics and Hydrodynamics".

Deadline for manuscript submissions: closed (31 August 2021) | Viewed by 10523

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Special Issue Editors

Prof. Dr. Anargiros I. Delis
E-Mail Website
Guest Editor
School of Production Engineering & Management, Technical University of Crete, Chania, 73100 Crete, Greece
Interests: computational mathematics; free surface flows; shallow water and Boussinesq-type equations; numerical methods
Prof. Dr. Ioannis K. Nikolos
E-Mail Website
Guest Editor
School of Production Engineering & Management, Technical University of Crete, Chania, Crete, 73100, GREECE
Interests: Computational Fluid Dynamics; Free surface flows; Aerodynamics; Numerical methods

Special Issue Information

Dear Colleagues,

In hydraulic engineering free surface water flows are commonly described by means of the shallow water equations (also called the Saint-Venant equations) and closely related models. Despite their simplicity, this description is valid in many applications in hydraulics and as such has a long tradition of providing a scientific basis for engineering practice. To this end, shallow water equations arise in modelling water flows in rivers, canals, lakes, reservoirs, coastal and urban areas and many other situations in which the water depth is much smaller than the horizontal length scale of motion. As such, shallow water and closely related equations are widely used in oceanography and atmospheric sciences to model, among others, hazardous phenomena as hurricanes/typhoons and tsunamis.

This Special Issue aims to provide a forum for the latest advanses in hydraulic modeling based on the use of shallow water and related models as well as their novel application in practical engineering. Original contributions in the following areas, though not exclusively, will be considered for publication: new conseptual models and applications, flood inundation and routing, sedimend transport and morphodynamic modelling, pollutant transport in water, irrigation and drainage modeling, numerical simulation in hydraulics, novel numerical methods for the shallow water equations and extended models, case studies, and high-performance computing.

Prof. Dr. Anargiros I. Delis
Prof. Dr. Ioannis K. Nikolos
Guest Editors

Manuscript Submission Information

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Keywords

  • Shallow water equations
  • Free surface flows
  • Hydraulic Engineering
  • Environmental Hydraulics
  • Computational Methods
  • Modeling
  • Simulation

Published Papers (8 papers)

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Editorial

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Editorial
Shallow Water Equations in Hydraulics: Modeling, Numerics and Applications
Water 2021, 13(24), 3598; https://doi.org/10.3390/w13243598 - 15 Dec 2021
Viewed by 732
Abstract
This Special Issue aimed to provide a forum for the latest advances in hydraulic modeling based on the use of non-linear shallow water equations (NSWEs) and closely related models, as well for their novel applications in practical engineering. NSWEs play a critical role [...] Read more.
This Special Issue aimed to provide a forum for the latest advances in hydraulic modeling based on the use of non-linear shallow water equations (NSWEs) and closely related models, as well for their novel applications in practical engineering. NSWEs play a critical role in the modeling and simulation of free surface flows in rivers and coastal areas and can predict tides, storm surge levels and coastline changes from hurricanes and ocean currents. NSWEs also arise in atmospheric flows, debris flows, internal flows and certain hydraulic structures such as open channels and reservoirs. Due to the important scientific value of NSWEs, research on effective and accurate numerical methods for their solutions has attracted great attention in the past two decades. Therefore, in this Special issue, original contributions in the following areas, though not exclusively, have been considered: new conceptual models and applications; flood inundation and routing; open channel flows; irrigation and drainage modeling; numerical simulation in hydraulics; novel numerical methods for shallow water equations and extended models; case studies; and high-performance computing. Full article

Research

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Article
Efficient Reservoir Modelling for Flood Regulation in the Ebro River (Spain)
Water 2021, 13(22), 3160; https://doi.org/10.3390/w13223160 - 09 Nov 2021
Cited by 2 | Viewed by 662
Abstract
The vast majority of reservoirs, although built for irrigation and water supply purposes, are also used as regulation tools during floods in river basins. Thus, the selection of the most suitable model when facing the simulation of a flood wave in a combination [...] Read more.
The vast majority of reservoirs, although built for irrigation and water supply purposes, are also used as regulation tools during floods in river basins. Thus, the selection of the most suitable model when facing the simulation of a flood wave in a combination of river reach and reservoir is not direct and frequently some analysis of the proper system of equations and the number of solved flow velocity components is needed. In this work, a stretch of the Ebro River (Spain), which is the biggest river in Spain, is simulated solving the Shallow Water Equations (SWE). The simulation model covers the area of river between the city of Zaragoza and the Mequinenza dam. The domain encompasses 721.92 km2 with 221 km of river bed, of which the last 75 km belong to the Mequinenza reservoir. The results obtained from a one-dimensional (1D) model are validated comparing with those provided by a two-dimensional (2D) model based on the same numerical scheme and with measurements. The 1D modelling loses the detail of the floodplain, but nevertheless the computational consumption is much lower compared to the 2D model with a permissible loss of accuracy. Additionally, the particular nature of this reservoir might turn the 1D model into a more suitable option. An alternative technique is applied in order to model the reservoir globally by means of a volume balance (0D) model, coupled to the 1D model of the river (1D-0D model). The results obtained are similar to those provided by the full 1D model with an improvement on computational time. Finally, an automatic regulation is implemented by means of a Proportional-Integral-Derivative (PID) algorithm and tested in both the full 1D model and the 1D-0D model. The results show that the coupled model behaves correctly even when controlled by the automatic algorithm. Full article
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Article
An Optimized and Scalable Algorithm for the Fast Convergence of Steady 1-D Open-Channel Flows
Water 2020, 12(11), 3218; https://doi.org/10.3390/w12113218 - 17 Nov 2020
Cited by 1 | Viewed by 655
Abstract
Calculating an open-channel steady flow is of main interest in many situations; this includes defining the initial conditions for the unsteady simulation or the computation of the water level for a given discharge. There are several applications that require a very short computation [...] Read more.
Calculating an open-channel steady flow is of main interest in many situations; this includes defining the initial conditions for the unsteady simulation or the computation of the water level for a given discharge. There are several applications that require a very short computation time in order to envisage a large number of runs, for example, uncertainty analysis or optimization. Here, an optimized algorithm was implemented for the fast and efficient computation of a 1-D steady flow. It merges several techniques: a pseudo-time version of the Saint-Venant equations, an evolutionary domain and the use of a non-linear Krylov accelerator. After validation of this new algorithm, we also showed that it performs well in scalability tests. The computation cost evolves linearly with the number of nodes. This was also corroborated when the execution time was compared to that obtained by the non-linear solver, CasADi. A real-world example using a 9.5 km stretch of river confirmed that the computation times were very short compared to a standard time-dependent computation. Full article
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Article
Numerical and Experimental Study of Classical Hydraulic Jump
Water 2020, 12(6), 1766; https://doi.org/10.3390/w12061766 - 21 Jun 2020
Cited by 5 | Viewed by 1247
Abstract
The present work is an effort to simulate numerically a classical hydraulic jump in a horizontal open channel with a rectangular cross-section, as far as the jump location and free surface elevation is concerned, and compare the results to experiments with Froude numbers [...] Read more.
The present work is an effort to simulate numerically a classical hydraulic jump in a horizontal open channel with a rectangular cross-section, as far as the jump location and free surface elevation is concerned, and compare the results to experiments with Froude numbers in the range 2.44 to 5.38. The governing equations describing the unsteady one-dimensional rapidly varied flow have been solved with the assumption of non-hydrostatic pressure distribution. Two finite difference schemes were used for the discretization of the mass and momentum conservation equations, along with the appropriate initial and boundary conditions. The method of specified intervals has been employed for the calculation of the velocity at the downstream boundary node. Artificial viscosity was required for damping the oscillations near the steep gradients of the jump. An iterative algorithm was used to minimize the difference of flow depth between two successive iterations that must be less than a threshold value, for achieving steady state solution. The time interval varied in each iteration as a function of the Courant number for stability reasons. Comparison of the numerical results with experiments showed the validity of the computations. The numerical codes have been implemented in house using a Matlab® environment. Full article
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Article
Effect of Open Boundary Conditions and Bottom Roughness on Tidal Modeling around the West Coast of Korea
Water 2020, 12(6), 1706; https://doi.org/10.3390/w12061706 - 15 Jun 2020
Cited by 4 | Viewed by 1021
Abstract
The aim of this study was to investigate the effect of open boundary conditions and bottom roughness on the tidal elevations around the West Coast of Korea (WCK) using an open-source computational fluids dynamics tool, the TELEMAC model. To obtain a detailed tidal [...] Read more.
The aim of this study was to investigate the effect of open boundary conditions and bottom roughness on the tidal elevations around the West Coast of Korea (WCK) using an open-source computational fluids dynamics tool, the TELEMAC model. To obtain a detailed tidal forcing at open boundaries, three well-known assimilated tidal models—the Finite Element Solution (FES2014), the Oregon State University TOPEX/Poseidon Global Inverse Solution Tidal Model (TPXO9.1) and the National Astronomical Observatory of Japan (NAO.99Jb)—have been applied to interpolate the offshore tidal boundary conditions. A number of numerical simulations have been performed for different offshore open boundary conditions, as well as for various uniform and non-uniform bottom roughness coefficients. The numerical results were calibrated against observations to determine the best fit roughness values for different sub-regions within WCK. In order to find out the dependence of the tidal elevation around the WCK on the variations of open boundary forcing, a sensitivity analysis of coastal tide elevation was carried out. Consequently, it showed that the tidal elevation around the WCK was strongly affected by local characteristics, rather than by the offshore open boundary conditions. Eventually, the numerical results can provide better quantitative and qualitative tidal information around the WCK than the data obtained from assimilated tidal models. Full article
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Article
Implementation of a Local Time Stepping Algorithm and Its Acceleration Effect on Two-Dimensional Hydrodynamic Models
Water 2020, 12(4), 1148; https://doi.org/10.3390/w12041148 - 17 Apr 2020
Cited by 3 | Viewed by 921
Abstract
The engineering applications of two-dimensional (2D) hydrodynamic models are restricted by the enormous number of meshes needed and the overheads of simulation time. The aim of this study is to improve computational efficiency and optimize the balance between the quantity of grids used [...] Read more.
The engineering applications of two-dimensional (2D) hydrodynamic models are restricted by the enormous number of meshes needed and the overheads of simulation time. The aim of this study is to improve computational efficiency and optimize the balance between the quantity of grids used in and the simulation accuracy of 2D hydrodynamic models. Local mesh refinement and a local time stepping (LTS) strategy were used to address this aim. The implementation of the LTS algorithm on a 2D shallow-water dynamic model was investigated using the finite volume method on unstructured meshes. The model performance was evaluated using three canonical test cases, which discussed the influential factors and the adaptive conditions of the algorithm. The results of the numerical tests show that the LTS method improved the computational efficiency and fulfilled mass conservation and solution accuracy constraints. Speedup ratios of between 1.3 and 2.1 were obtained. The LTS scheme was used for navigable flow simulation of the river reach between the Three Gorges and Gezhouba Dams. This showed that the LTS scheme is effective for real complex applications and long simulations and can meet the required accuracy. An analysis of the influence of the mesh refinement on the speedup was conducted. Coarse and refined mesh proportions and mesh scales observably affected the acceleration effect of the LTS algorithm. Smaller proportions of refined mesh resulted in higher speedup ratios. Acceleration was the most obvious when mesh scale differences were large. These results provide technical guidelines for reducing computational time for 2D hydrodynamic models on non-uniform unstructured grids. Full article
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Article
2D Numerical Modeling on the Transformation Mechanism of the Braided Channel
Water 2019, 11(10), 2030; https://doi.org/10.3390/w11102030 - 28 Sep 2019
Cited by 1 | Viewed by 1111
Abstract
This paper investigates the transformation mechanism between different channel patterns. A developed 2D depth-averaged numerical model is improved to take into account a bank vegetation stress term in the momentum conservation equation of flow. Then, the extended 2D model is applied to duplicate [...] Read more.
This paper investigates the transformation mechanism between different channel patterns. A developed 2D depth-averaged numerical model is improved to take into account a bank vegetation stress term in the momentum conservation equation of flow. Then, the extended 2D model is applied to duplicate the evolution of channel pattern with variations in flow discharge, sediment supply and bank vegetation. Complex interaction among the flow discharge, sediment supply and bank vegetation leads to a transition from the braided pattern to the meandering one. Analysis of the simulation process indicates that (1) a decrease in the flow discharge and sediment supply can lead to the transition and (2) the riparian vegetation helps stabilize the cut bank and bar surface, but is not a key in the transition. The results are in agreement with the criterion proposed in the previous research, confirming the 2D numerical model’s potential in predicting the transition between different channel patterns and improving understanding of the fluvial process. Full article
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Article
Comparison of Shallow Water Solvers: Applications for Dam-Break and Tsunami Cases with Reordering Strategy for Efficient Vectorization on Modern Hardware
Water 2019, 11(4), 639; https://doi.org/10.3390/w11040639 - 27 Mar 2019
Cited by 14 | Viewed by 2373
Abstract
We investigate in this paper the behaviors of the Riemann solvers (Roe and Harten-Lax-van Leer-Contact (HLLC) schemes) and the Riemann-solver-free method (central-upwind scheme) regarding their accuracy and efficiency for solving the 2D shallow water equations. Our model was devised to be spatially second-order [...] Read more.
We investigate in this paper the behaviors of the Riemann solvers (Roe and Harten-Lax-van Leer-Contact (HLLC) schemes) and the Riemann-solver-free method (central-upwind scheme) regarding their accuracy and efficiency for solving the 2D shallow water equations. Our model was devised to be spatially second-order accurate with the Monotonic Upwind Scheme for Conservation Laws (MUSCL) reconstruction for a cell-centered finite volume scheme—and be temporally fourth-order accurate using the Runge–Kutta fourth-order method. Four benchmark cases of dam-break and tsunami events dealing with highly-discontinuous flows and wet–dry problems were simulated. To this end, we applied a reordering strategy for the data structures in our code supporting efficient vectorization and memory access alignment for boosting the performance. Two main features are pointed out here. Firstly, the reordering strategy employed has enabled highly-efficient vectorization for the three solvers investigated on three modern hardware (AVX, AVX2, and AVX-512), where speed-ups of 4.5–6.5× were obtained on the AVX/AVX2 machines for eight data per vector while on the AVX-512 machine we achieved a speed-up of up to 16.7× for 16 data per vector, all with singe-core computation; with parallel simulations, speed-ups of up to 75.7–121.8× and 928.9× were obtained on AVX/AVX2 and AVX-512 machines, respectively. Secondly, we observed that the central-upwind scheme was able to outperform the HLLC and Roe schemes 1.4× and 1.25×, respectively, by exhibiting similar accuracies. This study would be useful for modelers who are interested in developing shallow water codes. Full article
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