Nested numerical scheme in a polar coordinate shallow water model for the coast of Bangladesh

2012 ◽  
Vol 17 (1) ◽  
pp. 37-47 ◽  
Author(s):  
M. Mizanur Rahman ◽  
Gour Chandra Paul ◽  
Ashabul Hoque
Keyword(s):  
Shallow Water ◽  
Numerical Scheme ◽  
Water Model ◽  
Shallow Water Model ◽  
Polar Coordinate

scholarly journals Eastward-moving convection-enhanced modons in shallow water in the equatorial tangent plane

2019 ◽  
Author(s):  
M. Rostami
Keyword(s):  
Shallow Water ◽  
Numerical Scheme ◽  
Large Scale ◽  
Tangent Plane ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Beta Plane ◽  
Vapour Condensation ◽  
Velocity Approximation

We report a discovery of steady long-living slowly eastward moving large-scale coherent twin cyclones, the equatorial modons, in the shallow water model in the equatorial beta-plane, the archetype model of the ocean and atmosphere dynamics in tropics. We start by constructing analytical asymptotic modon solutions in the non-divergent velocity approximation and then show by simulations with a high-resolution numerical scheme that such configurations evolve into steady dipolar solutions of the full model. In the atmospheric context, the modons persist in the presence of moist convection, being accompanied and enhanced by specific patterns of water-vapour condensation.

ON A BI-LAYER SHALLOW WATER MODEL WITH RIGID-LID HYPOTHESIS

2005 ◽  
Vol 15 (06) ◽  
pp. 843-869 ◽  
Author(s):  
B. DI MARTINO ◽  
P. ORENGA ◽  
M. PEYBERNES
Keyword(s):  
Shallow Water ◽  
Numerical Scheme ◽  
Water Model ◽  
Computational Time ◽  
Shallow Water Model ◽  
Layer Model ◽  
Water Problem ◽  
Existence And Regularity Results ◽  
Comparative Results ◽  
Regularity Results

In this paper, we present a new model for a bi-layer shallow water problem using the rigid-lid hypothesis. This model follows from the usual bi-layer model and can drastically decrease the computational time of simulation. But some mathematical and numerical difficulties appear. Particularly, we observe in the equations some terms in the form of 1/hi (where hi is the thickness of the layer) and we are not able to prove that hi > 0. To circumvent this difficulty, we replace in these terms hi by Hi > β > 0, where Hi is a characteristic thickness of the layer. This hypothesis is realistic if the fluctuations of hi are small, which is generally the case. Then, we prove existence and regularity results for this approximated problem which shows the convergence of the numerical scheme. Next, we present some comparative results in an idealized configuration between this model and the classical bi-layer shallow water model.

scholarly journals An Arbitrary High Order Well-Balanced ADER-DG Numerical Scheme for the Multilayer Shallow-Water Model with Variable Density

2021 ◽  
Vol 90 (1) ◽  
Author(s):  
E. Guerrero Fernández ◽  
M. J. Castro Díaz ◽  
M. Dumbser ◽  
T. Morales de Luna
Keyword(s):  
Shallow Water ◽  
Numerical Scheme ◽  
Stationary Solutions ◽  
Variable Density ◽  
High Order ◽  
Water Model ◽  
Variable Pressure ◽  
Shallow Water Model ◽  
Hyperbolic Pde ◽  
Coarse Meshes

AbstractIn this work, we present a novel numerical discretization of a variable pressure multilayer shallow water model. The model can be written as a hyperbolic PDE system and allows the simulation of density driven gravity currents in a shallow water framework. The proposed discretization consists in an unlimited arbitrary high order accurate (ADER) Discontinuous Galerkin (DG) method, which is then limited with the MOOD paradigm using an a posteriori subcell finite volume limiter. The resulting numerical scheme is arbitrary high order accurate in space and time for smooth solutions and does not destroy the natural subcell resolution inherent in the DG methods in the presence of strong gradients or discontinuities. A numerical strategy to preserve non-trivial stationary solutions is also discussed. The final method is very accurate in smooth regions even using coarse or very coarse meshes, as shown in the numerical simulations presented here. Finally, a comparison with a laboratory test, where empirical data are available, is also performed.

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.

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