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

2004 ◽  
Author(s):  
F. STURM
Keyword(s):  
Parabolic Equation ◽  
Shallow Water ◽  
Equation Model ◽  
Test Case

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

2001 ◽  
Vol 09 (01) ◽  
pp. 243-285 ◽  
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.

THE USE OF TESSELLATION IN THREE-DIMENSIONAL PARABOLIC EQUATION MODELING

2011 ◽  
Vol 19 (03) ◽  
pp. 221-239 ◽  
Author(s):  
MELANIE E. AUSTIN ◽  
N. ROSS CHAPMAN
Keyword(s):  
Parabolic Equation ◽  
Horizontal Plane ◽  
Three Dimensional ◽  
Computation Time ◽  
Equation Model ◽  
Equation Modeling ◽  
Test Case ◽  
Benchmark Test ◽  
Grid Points ◽  
Grid Layout

A full three-dimensional parabolic equation model (MONM3D) has been developed that incorporates techniques that reduce the required number of model grid points and reduces computation time. The concept of tessellation is implemented in MONM3D, which allows the number of radial paths in the model grid to vary with range from the source, reducing the number of computational points in the horizontal plane. This design establishes a grid layout that is both numerically and computationally desirable. A benchmark test case is used to illustrate the accuracy and efficiency of the model.

scholarly journals A test case for the inviscid shallow-water equations on the sphere

2015 ◽  
Vol 142 (694) ◽  
pp. 488-495 ◽  
Author(s):  
R. K. Scott ◽  
L. M. Harris ◽  
L. M. Polvani
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Test Case

Predicting mesh density for adaptive modelling of the global atmosphere

2009 ◽  
Vol 367 (1907) ◽  
pp. 4523-4542 ◽  
Author(s):  
Hilary Weller
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Large Scale ◽  
Mesh Adaptation ◽  
Similar Proportion ◽  
Test Case ◽  
Uniform Mesh ◽  
Coarse Mesh ◽  
Mesh Density ◽  
The Cost

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.

scholarly journals A GPU-based 2D shallow water quality model

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.

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

1999 ◽  
Vol 396 ◽  
pp. 223-256 ◽  
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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