Energy-Stable Residual Distribution Methods For System Of Shallow Water Equations

A state-of-the-art Energy-Stable Residual Distribution (ESRD) method is expanded for a system of Shallow Water Equations (SWE) as an improvement over the finite volume counterpart (ESFV) for inheriting multi-dimensional feature, minimal sensitivity to grid distortions and the ability to achieve high...

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Main Author:	Wei Shyang, Chang
Format:	Thesis
Language:	English
Published:	2019
Subjects:	T Technology
Online Access:	http://eprints.usm.my/56207/1/Energy-Stable%20Residual%20Distribution%20Methods%20For%20System%20Of%20Shallow%20Water%20Equations_Chang%20Wei%20Shyang.pdf
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spelling	my-usm-ep.562072023-01-03T09:08:54Z Energy-Stable Residual Distribution Methods For System Of Shallow Water Equations 2019-01-01 Wei Shyang, Chang T Technology TL Motor vehicles. Aeronautics. Astronautics A state-of-the-art Energy-Stable Residual Distribution (ESRD) method is expanded for a system of Shallow Water Equations (SWE) as an improvement over the finite volume counterpart (ESFV) for inheriting multi-dimensional feature, minimal sensitivity to grid distortions and the ability to achieve higher order accuracy with smaller stencil. ESRD imposes energy control simultaneously with the computation of the main variables through the mapping of primary conservative variables to energy variables. The energy conservation and energy stable conditions are achieved via the design of isotropic signals and artificial signals respectively. To preserve the cost-effectiveness of the scheme, the work is limited to only full explicit approach. The main contribution of this work is the source term discretisation which is designed to achieve numerical well-balanceness property. The effects of grid skewness variations on the order of accuracy and stability of ESRD were examined based on scalar analyses. Different degrees of freedom were manipulated to achieve positivity (first order scheme) and linear preserving (second order scheme) properties. A non-linear limited scheme is also constructed with the blending of the first and second order schemes. Unlike ESFV, ESRD demonstrates its ability to preserve the order of accuracy even on high randomized triangular grids. The well-balancedness of the proposed scheme was validated numerically and the order of accuracy of the well-balanced version of the schemes are still preserved. 2019-01 Thesis http://eprints.usm.my/56207/ http://eprints.usm.my/56207/1/Energy-Stable%20Residual%20Distribution%20Methods%20For%20System%20Of%20Shallow%20Water%20Equations_Chang%20Wei%20Shyang.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Kejuruteraan Aeroangkasa
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
language	English
topic	T Technology T Technology
spellingShingle	T Technology T Technology Wei Shyang, Chang Energy-Stable Residual Distribution Methods For System Of Shallow Water Equations
description	A state-of-the-art Energy-Stable Residual Distribution (ESRD) method is expanded for a system of Shallow Water Equations (SWE) as an improvement over the finite volume counterpart (ESFV) for inheriting multi-dimensional feature, minimal sensitivity to grid distortions and the ability to achieve higher order accuracy with smaller stencil. ESRD imposes energy control simultaneously with the computation of the main variables through the mapping of primary conservative variables to energy variables. The energy conservation and energy stable conditions are achieved via the design of isotropic signals and artificial signals respectively. To preserve the cost-effectiveness of the scheme, the work is limited to only full explicit approach. The main contribution of this work is the source term discretisation which is designed to achieve numerical well-balanceness property. The effects of grid skewness variations on the order of accuracy and stability of ESRD were examined based on scalar analyses. Different degrees of freedom were manipulated to achieve positivity (first order scheme) and linear preserving (second order scheme) properties. A non-linear limited scheme is also constructed with the blending of the first and second order schemes. Unlike ESFV, ESRD demonstrates its ability to preserve the order of accuracy even on high randomized triangular grids. The well-balancedness of the proposed scheme was validated numerically and the order of accuracy of the well-balanced version of the schemes are still preserved.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Wei Shyang, Chang
author_facet	Wei Shyang, Chang
author_sort	Wei Shyang, Chang
title	Energy-Stable Residual Distribution Methods For System Of Shallow Water Equations
title_short	Energy-Stable Residual Distribution Methods For System Of Shallow Water Equations
title_full	Energy-Stable Residual Distribution Methods For System Of Shallow Water Equations
title_fullStr	Energy-Stable Residual Distribution Methods For System Of Shallow Water Equations
title_full_unstemmed	Energy-Stable Residual Distribution Methods For System Of Shallow Water Equations
title_sort	energy-stable residual distribution methods for system of shallow water equations
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Kejuruteraan Aeroangkasa
publishDate	2019
url	http://eprints.usm.my/56207/1/Energy-Stable%20Residual%20Distribution%20Methods%20For%20System%20Of%20Shallow%20Water%20Equations_Chang%20Wei%20Shyang.pdf
_version_	1776101151336300544

Energy-Stable Residual Distribution Methods For System Of Shallow Water Equations

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