Modelling the effect of proposed channel deepening on the tides in Port Phillip Bay

Sampson, Joe; Easton, Alan K.; Singh, Manmohan

doi:10.21914/anziamj.v46i0.996

Cited by 2 publications

(3 citation statements)

References 3 publications

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“…In the meanwhile, the set of shallow water equations (though younger, as the equations have been written by Adhémar Barré de Saint-Venant in 1871 [18]) have received a large audience as well. They are used for modelling the flow in rivers [31], [12] (and networks of rivers), in lakes, rain overland flow [20,21], [75], in dams [77,78] or the long waves in shallow water seas (tides in the Channel for example [70], or for Tsunami modelling [23], [68]). It has been observed that Saint-Venant equations with source terms (which are the shape of the topography, and the viscous terms) present numerical difficulties for steady states.…”

Section: Introductionmentioning

confidence: 99%

A ‘well‐balanced’ finite volume scheme for blood flow simulation

Delestre

Lagrée

2012

Numerical Methods in Fluids

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SUMMARYWe are interested in simulating blood flow in arteries with a one‐dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the Saint‐Venant shallow water equations context) we will perform a simple finite volume scheme. We focus on conservation properties of this scheme, which were not previously considered. To emphasize the necessity of this scheme, we present how a too simple numerical scheme may induce spurious flows when the basic static shape of the radius changes. On the contrary, the proposed scheme is ‘well‐balanced’: it preserves equilibria of Q = 0. Then examples of analytical or linearized solutions with and without viscous damping are presented to validate the calculations. The influence of abrupt change of basic radius is emphasized in the case of an aneurism. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

A ‘well‐balanced’ finite volume scheme for blood flow simulation

Delestre

Lagrée

2012

Numerical Methods in Fluids

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“…The Riemann solvers E f HLL and E g HLL in Equations (10) and (11) are computed using the HLL Riemann solver, which was developed by Harten, Lax, and Van Leer [21] described as follows:…”

Section: Approximated Riemann Solvermentioning

confidence: 99%

“…Fiedler and Ramirez are the first to use finite volume methods (FVMs), and Delestre and team are the first to use well‐balanced schemes for rainwater overland flow modeling. The other related applications for hyperbolic problems are dam break , tsunami , river flow , and tides .…”

Section: Introductionmentioning

confidence: 99%

Dynamically adaptive tree grid modeling for simulation and visualization of rainwater overland flow

Busaman

Mekchay

Siripant

et al. 2015

Numerical Methods in Fluids

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Summary Modeling and visualization of a rainwater overland flow is an important tool for a risk assessment, preparation, evacuation planning, and real‐time forecasting of flood warning. The objective of this research is to develop a numerical software to visualize the rainwater overland flow based on a finite volume method for shallow water equations and in combination with the dynamically adaptive tree grid technique and the dynamic domain‐defining method. The obtained simulations for several experiments were tested and compared with results in literature, both theoretical and experimental results. The comparisons with non‐adaptive grids show that the developed algorithm for simulation is very efficient and has a potential for practical usages, in terms of computational times and accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

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Modelling the effect of proposed channel deepening on the tides in Port Phillip Bay

Cited by 2 publications

References 3 publications

A ‘well‐balanced’ finite volume scheme for blood flow simulation

A ‘well‐balanced’ finite volume scheme for blood flow simulation

Dynamically adaptive tree grid modeling for simulation and visualization of rainwater overland flow

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