scholarly journals Local Well-Posedness of the Two-Layer Shallow Water Model with Free Surface

2015 ◽  
Vol 75 (5) ◽  
pp. 2311-2332 ◽  
Author(s):  
Ronan Monjarret
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Water Model ◽  
Well Posedness ◽  
Shallow Water Model

scholarly journals Simulation of Ocean Circulation of Dongsha Water Using Non-Hydrostatic Shallow-Water Model

Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2832 ◽  
Author(s):  
Shin-Jye Liang ◽  
Chih-Chieh Young ◽  
Chi Dai ◽  
Nan-Jing Wu ◽  
Tai-Wen Hsu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Free Surface ◽  
Hydrostatic Pressure ◽  
Velocity Field ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Shallow Water Model

A two-dimensional non-hydrostatic shallow-water model for weakly dispersive waves is developed using the least-squares finite-element method. The model is based on the depth-averaged, nonlinear and non-hydrostatic shallow-water equations. The non-hydrostatic shallow-water equations are solved with the semi-implicit (predictor-corrector) method and least-squares finite-element method. In the predictor step, hydrostatic pressure at the previous step is used as an initial guess and an intermediate velocity field is calculated. In the corrector step, a Poisson equation for the non-hydrostatic pressure is solved and the final velocity and free-surface elevation is corrected for the new time step. The non-hydrostatic shallow-water model is verified and applied to both wave and flow driven fluid flows, including solitary wave propagation in a channel, progressive sinusoidal waves propagation over a submerged bar, von Karmann vortex street, and ocean circulations of Dongsha Atolls. It is found hydrostatic shallow-water model is efficient and accurate for shallow water flows. Non-hydrostatic shallow-water model requires 1.5 to 3.0 more cpu time than hydrostatic shallow-water model for the same simulation. Model simulations reveal that non-hydrostatic pressure gradients could affect the velocity field and free-surface significantly in case where nonlinearity and dispersion are important during the course of wave propagation.

Three-dimensional flow evolution after a dam break

2010 ◽  
Vol 663 ◽  
pp. 456-477 ◽  
Author(s):  
A. FERRARI ◽  
L. FRACCAROLLO ◽  
M. DUMBSER ◽  
E. F. TORO ◽  
A. ARMANINI
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Shallow Water ◽  
Three Dimensional ◽  
Dam Break ◽  
Water Model ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Shallow Water Model ◽  
Weakly Compressible

In this paper, the wave propagation on a plane dry bottom after a dam break is analysed. Two mathematical models have been used and compared with each other for simulating such a dam-break scenario. First, the fully three-dimensional Navier–Stokes equations for a weakly compressible fluid have been solved using the new smooth particle hydrodynamics formulation, recently proposed by Ferrari et al. (Comput. Fluids, vol. 38, 2009, p. 1203). Second, the two-dimensional shallow water equations (SWEs) are solved using a third-order weighted essentially non-oscillatory finite-volume scheme. The numerical results are critically compared against the laboratory measurements provided by Fraccarollo & Toro (J. Hydraul. Res., vol. 33, 1995, p. 843). The experimental data provide the temporal evolution of the pressure field, the water depth and the vertical velocity profile at 40 gauges, located in the reservoir and in front of the gate. Our analysis reveals the shortcomings of SWEs in the initial stages of the dam-break phenomenon in reproducing many important flow features of the unsteady free-surface flow: the shallow water model predicts a complex wave structure and a wavy evolution of local free-surface elevations in the reservoir that can be clearly identified to be only model artefacts. However, the quasi-incompressible Navier–Stokes model reproduces well the high gradients in the flow field and predicts the cycles of simultaneous rapid decreasing and frozen stages of the free surface in the tank along with the velocity oscillations. Asymptotically, i.e. for ‘large times’, the shallow water model and the weakly compressible Navier–Stokes model agree well with the experimental data, since the classical SWE assumptions are satisfied only at large times.

The instability of vertically curved fronts in a two-layer shallow water model

2020 ◽  
Vol 32 (12) ◽  
pp. 124117
Author(s):  
M. W. Harris ◽  
F. J. Poulin ◽  
K. G. Lamb
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Shallow Water Model

scholarly journals Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2152
Author(s):  
Gonzalo García-Alén ◽  
Olalla García-Fonte ◽  
Luis Cea ◽  
Luís Pena ◽  
Jerónimo Puertas
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Experimental Dataset ◽  
River Hydraulics ◽  
Shallow Water Models ◽  
Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

scholarly journals Development of a Practical Model for Predicting Soil Salinity in a Salt Marsh in the Arakawa River Estuary

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2054
Author(s):  
Naoki Kuroda ◽  
Katsuhide Yokoyama ◽  
Tadaharu Ishikawa
Keyword(s):  
Salt Marsh ◽  
Hydraulic Conductivity ◽  
Shallow Water ◽  
Soil Salinity ◽  
River Estuary ◽  
Flow Simulation ◽  
Design Tool ◽  
Water Model ◽  
Shallow Water Model ◽  
Practical Model

Our group has studied the spatiotemporal variation of soil and water salinity in an artificial salt marsh along the Arakawa River estuary and developed a practical model for predicting soil salinity. The salinity of the salt marsh and the water level of a nearby channel were measured once a month for 13 consecutive months. The vertical profile of the soil salinity in the salt marsh was measured once monthly over the same period. A numerical flow simulation adopting the shallow water model faithfully reproduced the salinity variation in the salt marsh. Further, we developed a soil salinity model to estimate the soil salinity in a salt marsh in Arakawa River. The vertical distribution of the soil salinity in the salt marsh was uniform and changed at almost the same time. The hydraulic conductivity of the soil, moreover, was high. The uniform distribution of salinity and high hydraulic conductivity could be explained by the vertical and horizontal transport of salinity through channels burrowed in the soil by organisms. By combining the shallow water model and the soil salinity model, the soil salinity of the salt marsh was well reproduced. The above results suggest that a stable brackish ecotone can be created in an artificial salt marsh using our numerical model as a design tool.

Diffusion Experiments with a Global Discontinuous Galerkin Shallow-Water Model

2009 ◽  
Vol 137 (10) ◽  
pp. 3339-3350 ◽  
Author(s):  
Ramachandran D. Nair
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Water Model ◽  
Order System ◽  
Small Scale ◽  
Shallow Water Model ◽  
First Order ◽  
Advection Diffusion Equation ◽  
Diffusion Scheme ◽  
Cubed Sphere

Abstract A second-order diffusion scheme is developed for the discontinuous Galerkin (DG) global shallow-water model. The shallow-water equations are discretized on the cubed sphere tiled with quadrilateral elements relying on a nonorthogonal curvilinear coordinate system. In the viscous shallow-water model the diffusion terms (viscous fluxes) are approximated with two different approaches: 1) the element-wise localized discretization without considering the interelement contributions and 2) the discretization based on the local discontinuous Galerkin (LDG) method. In the LDG formulation the advection–diffusion equation is solved as a first-order system. All of the curvature terms resulting from the cubed-sphere geometry are incorporated into the first-order system. The effectiveness of each diffusion scheme is studied using the standard shallow-water test cases. The approach of element-wise localized discretization of the diffusion term is easy to implement but found to be less effective, and with relatively high diffusion coefficients, it can adversely affect the solution. The shallow-water tests show that the LDG scheme converges monotonically and that the rate of convergence is dependent on the coefficient of diffusion. Also the LDG scheme successfully eliminates small-scale noise, and the simulated results are smooth and comparable to the reference solution.

Sign in / Sign up

Export Citation Format

Share Document