Numerical Solution of the Rotating Shallow Water Flows with Topography Using the Fractional Steps Method

Hassan, Hossam S.; Ramadan, Khaled T.; Hanna, Sarwat N.

doi:10.4236/am.2010.12014

Cited by 9 publications

(8 citation statements)

References 22 publications

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“…Numerical hydrodynamic lake models have recently been used to address environmental problems as well as hydro-meteorological properties and geographical geometric characteristics [25]. The numerical model is solved by the SWEs and considers the Coriolis effect for lake bottom topography [26,27]. In Lake Victoria, Coriolis effects play less of a role because the lake is situated on the equator.…”

Section: Methodological Approachmentioning

confidence: 99%

Bathymetry Development and Flow Analyses Using Two-Dimensional Numerical Modeling Approach for Lake Victoria

Paul

Oppelstrup

Thunvik

et al. 2019

Fluids

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This study explored two-dimensional (2D) numerical hydrodynamic model simulations of Lake Victoria. Several methods were developed in Matlab to build the lake topography. Old depth soundings taken in smaller parts of the lake were combined with more recent extensive data to produce a smooth topographical model. The lake free surface numerical model in the COMSOL Multiphysics (CM) software was implemented using bathymetry and vertically integrated 2D shallow water equations. Validated by measurements of mean lake water level, the model predicted very low mean flow speeds and was thus close to being linear and time invariant, allowing long-time simulations with low-pass filtered inflow data. An outflow boundary condition allowed an accurate simulation to achieve the lake’s steady state level. The numerical accuracy of the linear measurement of lake water level was excellent.

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Section: Methodological Approachmentioning

confidence: 99%

Bathymetry Development and Flow Analyses Using Two-Dimensional Numerical Modeling Approach for Lake Victoria

Paul

Oppelstrup

Thunvik

et al. 2019

Fluids

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“…It is well-known that the shallow water equations may lead to the breaking waves due to the nonlinearity of the governed equations. By the existing researching works, for example, see [4,13], the appearance of breaking waves depends on many factors, among…”

Section: Example 2 Consider the Trigonometric Type Initial Conditionmentioning

confidence: 99%

On the data assimilation of initial distribution for 2-dimensional shallow-water equation model

Zhang,

Liu

2024

Phys. Scr.

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The utilization of data assimilation (DA) techniques is prevalent in marine meteorology for the purpose of estimating the complete state of the system. This is done to address the practical limitations associated with measurement data, which can only be specified at finite number of discrete points within a limited domain. We develop an efficient DA algorithm to reconstruct the initial state of the shallow-water equations (SWE) within a 2-dimensional rectangular domain using sparse spatial measurement data. Our algorithm takes into account both the complete Coriolis force and the ocean bottom topography in the SWE model, resulting in accurate recovery of the initial status. After establishing the uniqueness of the solution to the nonlinear SWE with appropriate boundary conditions, we proceed to establish the conservation laws for the suitably defined energy quantity for this traveling wave system. This generalization of the known conservation laws for the simplified SWE system, which ignores the Coriolis force and topography, allows us to reveal the influence of nonconstant sea floor topography on wave propagation. In order to restore the initial state through the minimization of a cost functional using DA techniques, we proceed by deriving the adjoint problem for our iteration process. Additionally, we establish a discrete scheme for the governing equations in the Arakawa C-grid framework, from which we rigorously derive the error associated with energy conservation in discrete form. The numerical implementations are also provided to validate our proposed scheme through the verification of energy conservation and the reconstruction effect of the initial state for various configurations.

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“…In this work, we also choose to set the Coriolis force to zero; numerical investigations show that their impact was insignificant within the considered scales. The inclusion of such long scale physical effects is performed in [5][6][7][8] for instance.…”

Section: Introductionmentioning

confidence: 99%

A robust and well‐balanced scheme for the 2D Saint‐Venant system on unstructured meshes with friction source term

Duran

2015

Numerical Methods in Fluids

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SummaryIn the following lines, we propose a numerical scheme for the shallow‐water system supplemented by topography and friction source terms, in a 2D unstructured context. This work proposes an improved version of the well‐balanced and robust numerical model recently introduced by Duran et al. (J. Comp. Phys., 235, 565–586, 2013) for the pre‐balanced shallow‐water equations, accounting for varying topography. The present work aims at relaxing the robustness condition and includes a friction term. To this purpose, the scheme is modified using a recent method, entirely based on a modified Riemann solver. This approach preserves the robustness and well‐balanced properties of the original scheme and prevents unstable computations in the presence of low water depths. A series of numerical experiments are devoted to highlighting the performances of the resulting scheme. Simulations involving dry areas, complex geometry and topography are proposed to validate the stability of the numerical model in the neighbourhood of wet/dry transitions. Copyright © 2015 John Wiley & Sons, Ltd.

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Numerical Solution of the Rotating Shallow Water Flows with Topography Using the Fractional Steps Method

Cited by 9 publications

References 22 publications

Bathymetry Development and Flow Analyses Using Two-Dimensional Numerical Modeling Approach for Lake Victoria

Bathymetry Development and Flow Analyses Using Two-Dimensional Numerical Modeling Approach for Lake Victoria

On the data assimilation of initial distribution for 2-dimensional shallow-water equation model

A robust and well‐balanced scheme for the 2D Saint‐Venant system on unstructured meshes with friction source term

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