Energy-Stable Residual Distribution Methods For System Of Shallow Water Equations
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Date
2018-01-01
Authors
Chang, Wei Shyang
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
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.