Subbottom profiling in shallow water: The Akko 4 test case

The shallow water equations are solved using a mesh of polygons on the sphere, which adapts infrequently to the predicted future solution. Infrequent mesh adaptation reduces the cost of adaptation and load-balancing and will thus allow for more accurate mapping on adaptation. We simulate the growth of a barotropically unstable jet adapting the mesh every 12 h. Using an adaptation criterion based largely on the gradient of the vorticity leads to a mesh with around 20 per cent of the cells of a uniform mesh that gives equivalent results. This is a similar proportion to previous studies of the same test case with mesh adaptation every 1–20 min. The prediction of the mesh density involves solving the shallow water equations on a coarse mesh in advance of the locally refined mesh in order to estimate where features requiring higher resolution will grow, decay or move to. The adaptation criterion consists of two parts: that resolved on the coarse mesh, and that which is not resolved and so is passively advected on the coarse mesh. This combination leads to a balance between resolving features controlled by the large-scale dynamics and maintaining fine-scale features.

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A GPU-based 2D shallow water quality model

Journal of Hydroinformatics ◽

10.2166/hydro.2020.030 ◽

2020 ◽

Vol 22 (5) ◽

pp. 1182-1197

Author(s):

Geovanny Gordillo ◽

Mario Morales-Hernández ◽

I. Echeverribar ◽

Javier Fernández-Pato ◽

Pilar García-Navarro

Keyword(s):

Water Quality ◽

Shallow Water ◽

Graphics Processing Unit ◽

Temporal Distribution ◽

Water Quality Model ◽

Quality Analysis ◽

Test Case ◽

Processing Unit ◽

Quality Model ◽

Central Processing

Abstract In this study, a 2D shallow water flow solver integrated with a water quality model is presented. The interaction between the main water quality constituents included is based on the Water Quality Analysis Simulation Program. Efficiency is achieved by computing with a combination of a Central Processing Unit (CPU) and a Graphics Processing Unit (GPU) device. This technique is intended to provide robust and accurate simulations with high computation speedups with respect to a single-core CPU in real events. The proposed numerical model is evaluated in cases that include the transport and reaction of water quality components over irregular bed topography and dry–wet fronts, verifying that the numerical solution in these situations conserves the required properties (C-property and positivity). The model can operate in any steady or unsteady form allowing an efficient assessment of the environmental impact of water flows. The field data from an unsteady river reach test case are used to show that the model is capable of predicting the measured temporal distribution of dissolved oxygen and water temperature, proving the robustness and computational efficiency of the model, even in the presence of noisy signals such as wind speed.

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Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state

Journal of Fluid Mechanics ◽

10.1017/s0022112099006084 ◽

1999 ◽

Vol 396 ◽

pp. 223-256 ◽

Cited By ~ 49

Author(s):

B. S. BROOK ◽

S. A. E. G. FALLE ◽

T. J. PEDLEY

Keyword(s):

Shallow Water ◽

Numerical Solutions ◽

Godunov Method ◽

Test Case ◽

Interesting Phenomenon ◽

One Dimensional ◽

Collapsible Tubes ◽

Highly Nonlinear ◽

Pressure Area ◽

The One

Unsteady flow in collapsible tubes has been widely studied for a number of different physiological applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure–area relation for collapsible tubes.The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method.Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow.

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BROADBAND PROPAGATION RESULTS FOR A SHALLOW WATER GAUSSIAN CANYON TEST CASE USING A 3-D PARABOLIC EQUATION MODEL

Theoretical and Computational Acoustics 2003 ◽

10.1142/9789812702609_0033 ◽

2004 ◽

Author(s):

F. STURM

Keyword(s):

Parabolic Equation ◽

Shallow Water ◽

Equation Model ◽

Test Case

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The Diabatic Contour-Advective Semi-Lagrangian Algorithms for the Spherical Shallow Water Equations

Monthly Weather Review ◽

10.1175/2009mwr2717.1 ◽

2009 ◽

Vol 137 (9) ◽

pp. 2979-2994 ◽

Cited By ~ 8

Author(s):

Ali R. Mohebalhojeh ◽

David G. Dritschel

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Relative Strength ◽

Test Case ◽

Diagnostic Measures ◽

Contour Advection ◽

Rapid Generation ◽

Quasigeostrophic Model ◽

Conventional Algorithm ◽

Grid Based

Abstract The diabatic contour-advective semi-Lagrangian (DCASL) algorithm is extended to the thermally forced shallow water equations on the sphere. DCASL rests on the partitioning of potential vorticity (PV) to adiabatic and diabatic parts solved, respectively, by contour advection and a grid-based conventional algorithm. The presence of PV in the source term for diabatic PV makes the shallow water equations distinct from the quasigeostrophic model previously studied. To address the more rapid generation of finescale structures in diabatic PV, two new features are added to DCASL: (i) the use of multiple sets of contours with successively finer contour intervals and (ii) the application of the underlying method of DCASL at a higher level to diabatic PV. That is, the diabatic PV is allowed to have both contour and grid parts. The added features make it possible to make the grid part of diabatic PV arbitrarily small and thus pave the way for a fully Lagrangian DCASL in the presence of forcing. The DCASL algorithms are constructed using a standard semi-Lagrangian (SL) algorithm to solve for the grid-based part of diabatic PV. The 25-day time evolution of an unstable midlatitude jet triggered by the action of thermal forcing is used as a test case to examine and compare the properties of the DCASL algorithms with a pure SL algorithm for PV. Diagnostic measures of vortical and unbalanced activity as well as of the relative strength of the grid and contour parts of the solution for PV indicate that the superiority of contour advection can be maintained even in the presence of strong, nonsmooth forcing.

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Inland waterway ship test case for resistance and propulsion prediction in shallow water

Ship Technology Research ◽

10.1080/09377255.2017.1349723 ◽

2017 ◽

Vol 64 (2) ◽

pp. 106-113 ◽

Cited By ~ 2

Author(s):

Philipp Mucha ◽

Ould el Moctar ◽

Thorsten Dettmann ◽

Matthias Tenzer

Keyword(s):

Shallow Water ◽

Test Case ◽

Inland Waterway

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CONVERGENCE, STABILITY, AND VARIABILITY OF SHALLOW WATER ACOUSTIC PREDICTIONS USING A SPLIT-STEP FOURIER PARABOLIC EQUATION MODEL

Journal of Computational Acoustics ◽

10.1142/s0218396x01000401 ◽

2001 ◽

Vol 09 (01) ◽

pp. 243-285 ◽

Cited By ~ 43

Author(s):

KEVIN B. SMITH

Keyword(s):

Parabolic Equation ◽

Shallow Water ◽

Acoustic Field ◽

Equation Model ◽

Single Frequency ◽

Test Case ◽

Flat Bottom ◽

Parameter Variations ◽

Interface Boundary Conditions ◽

Fourier Algorithm

The Shallow Water Acoustic Modeling (SWAM'99) Workshop was organized to examine the ability of various acoustic propagation models to accurately predict sound transmission in a variety of shallow water environments designed with realistic perturbations. In order to quantify this, tests of reciprocity, convergence, and stability must be considered. This paper presents the results of an established parabolic equation model based on the split-step Fourier algorithm. The test cases examined in this paper include a simple isospeed water column over a flat bottom with geoacoustic parameter variations, a randomly sloping bottom with geoacoustic parameter variations, and a canonical shallow water profile perturbed by internal waves over a flat, homogeneous bottom. Source configurations were generally held constant but numerous single frequency and broadband runs were performed. Model testing is emphasized with specific criteria for accurate solutions being specified. Random perturbations are added to one test case to examine the influence of environmental uncertainty on the details of the propagation. The results indicate that point-wise accurate solutions to the acoustic field in shallow water cannot be achieved beyond a few kilometers. This is partly due to the inaccuracies of the split-step Fourier algorithm employed in these shallow water scenarios and the treatment of the bottom interface boundary conditions, but also due to the inherent variability caused by uncertain environmental specification. Thus, more general features of the acoustic field should be emphasized at longer ranges.

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Towards fast large-scale flood simulations using 2D Shallow water modelling with depth-dependant porosity

10.5194/egusphere-egu2020-11562 ◽

2020 ◽

Author(s):

Vita Ayoub ◽

Carole Delenne ◽

Patrick Matgen ◽

Pascal Finaud-Guyot ◽

Renaud Hostache

Keyword(s):

Shallow Water ◽

Spatial Data ◽

Large Scale ◽

Model Performance ◽

Water Model ◽

Computational Time ◽

Small Scale ◽

Test Case ◽

Strong Impact ◽

Flood Simulations

<p><span>In hydrodynamic modelling, the mesh resolution has a strong impact on run time and result accuracy. Coarser meshes allow faster simulations but often at the cost of accuracy. Conversely, finer meshes offer a better description of complex geometries but require much longer computational time, which makes their use at a large scale challenging. In this context, we aim to assess the potential of a two-dimensional shallow water model with depth-dependant porosity (SW2D-DDP) for flood simulations at a large scale. This modelling approach relies on nesting a sub-grid mesh containing high-resolution topographic and bathymetric data within each computational cell via a so-called depth-dependant storage porosity. It enables therefore faster simulations on rather coarse grids while preserving small-scale topography information. The July 2007 flood event in the Severn River basin (UK) is used as a test case, for which hydrometric measurements and spatial data are available for evaluation. A sensitivity analysis is carried out to investigate the porosity influence on the model performance in comparison with other classical parameters such as boundary conditions.</span></p>

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