A stable scheme of the Curvilinear Shallow Water Equations with no-penetration and far-field boundary conditions
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Date
2023-11-23
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Elsevier
Abstract
This paper presents a stable and highly accurate numerical tool for computing river flows in urban areas, which
is a first step towards a numerical tool for flood predictions. We start with the (linearized) well-posedness
analysis by Ghader and Nordström (2014), where far-field boundary conditions were proposed and extend
their analysis to include wall boundaries. Specifically, we employed high-order Summation-by-parts (SBP)
finite-difference operators to construct a scheme for the Shallow Water Equations. We also developed a stable
SBP scheme with Simultaneous Approximation Terms that impose far-field and wall boundaries. Finally, we
extended the schemes and their stability proofs to non-Cartesian domains. To demonstrate the strength of the
schemes, we performed computations for problems with exact solutions to obtain second, third, and fourth (2,
3, 4) convergence rates. Finally, we applied the 4𝑡ℎ-order scheme to steady river channels, the canal (or floodcontrol
channel simulations), and dam-break problems. The results show that the imposition of the boundary
conditions is stable, and the far-field boundaries cause no visible reflections at the boundaries.
Description
This article is published by Elsevier 2023 and is also available at https://doi.org/10.1016/j.compfluid.2023.106136
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Citation
R.N. Borkor et al.