Quadratic finite elements for the study of shallow water problems
Quadratic finite elements for the study of shallow water problems
After an examination of the derivation of the Shallow Water Equations and the assumptions involved, existing mathematical models for circulation problems, using finite difference and finite element methods, are considered. A new series of six node triangular finite element models are. proposed which are able to represent more accurately both the curved coastal boundaries and bottom topography. The models are tested on rectangular. channel problems, both to assess their suitability and to examine the influence of water depth, level of friction and the advective terms upon the results. It is shown that a finite difference type stability criterion predicts successfully the limiting timestep for the Explicit 4th order Runge Kutta model. TheImplicit Trapezoidal rule model may use a timestep related to the period time of the pro-Diem by an accuracy criterion.The first large scale problem considered is that of the Solent, an area of complicated bottom., topography. The limiting timestep for this situation is too small to allow the explicit model to be used economically. Results are obtained for different timesteps and conditions of friction from ~cold start~ conditions using the implicit modal.For the Worth Sea both models may be applied; results are presented 'or wave-height, circulation and residual currents under a variety of different conditions of timestep, friction ar_d tidal boundaryIt is concluded that better answers are obtained if attention is paid to the representation of bottom topography, if the level of friction is varied throughout the model accordingly, and if a smoothing tec.riau_ is applied to the answers obtained from the initial ~cold start~ z,inuation.Suggestions are made for improvement of opeed of solution and accuracy for f=are raodels.
University of Southampton
1976
Partridge, Paul William
(1976)
Quadratic finite elements for the study of shallow water problems.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
After an examination of the derivation of the Shallow Water Equations and the assumptions involved, existing mathematical models for circulation problems, using finite difference and finite element methods, are considered. A new series of six node triangular finite element models are. proposed which are able to represent more accurately both the curved coastal boundaries and bottom topography. The models are tested on rectangular. channel problems, both to assess their suitability and to examine the influence of water depth, level of friction and the advective terms upon the results. It is shown that a finite difference type stability criterion predicts successfully the limiting timestep for the Explicit 4th order Runge Kutta model. TheImplicit Trapezoidal rule model may use a timestep related to the period time of the pro-Diem by an accuracy criterion.The first large scale problem considered is that of the Solent, an area of complicated bottom., topography. The limiting timestep for this situation is too small to allow the explicit model to be used economically. Results are obtained for different timesteps and conditions of friction from ~cold start~ conditions using the implicit modal.For the Worth Sea both models may be applied; results are presented 'or wave-height, circulation and residual currents under a variety of different conditions of timestep, friction ar_d tidal boundaryIt is concluded that better answers are obtained if attention is paid to the representation of bottom topography, if the level of friction is varied throughout the model accordingly, and if a smoothing tec.riau_ is applied to the answers obtained from the initial ~cold start~ z,inuation.Suggestions are made for improvement of opeed of solution and accuracy for f=are raodels.
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Published date: 1976
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Local EPrints ID: 458285
URI: http://eprints.soton.ac.uk/id/eprint/458285
PURE UUID: 1fccae11-435c-423b-8d34-9bd26c319f63
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Date deposited: 04 Jul 2022 16:46
Last modified: 04 Jul 2022 16:46
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Author:
Paul William Partridge
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