Simulation of Shallow-water Flows in Complex Bay-like Domains

Yuri N. Skiba, Denis M. Filatov

2012

Abstract

A new numerical method for the simulation of shallow-water flows in a bay-like domain is suggested. The method is based on the splitting of the original nonlinear operator by physical processes and by coordinates. An essential advantage of our finite difference splitting-based method versus others in the field is that it leads to a model allowing accurate simulation of shallow-water flows in a domain of an arbitrary shape with both closed and open boundaries, which besides may contain onshore parts inside (interior isles in the bay); the model also takes into account irregular bottom topography. Specially constructed approximations of the temporal and spatial derivatives result in second-order unconditionally stable finite difference schemes that conserve the mass and the total energy of the discrete inviscid unforced shallow-water system. Moreover, the potential enstrophy results to be bounded, oscillating in time within a narrow range. Therefore, the numerical solution, aside from being accurate from the mathematical point of view, appears to be physically adequate, inheriting a number of substantial properties of the original differential shallow-water system. Furthermore, the method can straightforwardly be implemented for distributed simulation of shallow-water flows on high-performance parallel computers. To test the method numerically, we start with the inviscid shallow-water model and verify the conservatism of the schemes in a simple computational domain. Then we introduce a domain with a more complex boundary consisting of closed and open segments, and consider more realistic viscous wind-driven shallow-water flows. Numerical experiments presented confirm the skills of the developed method.

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Paper Citation


in Harvard Style

N. Skiba Y. and M. Filatov D. (2012). Simulation of Shallow-water Flows in Complex Bay-like Domains . In Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-8565-20-4, pages 24-31. DOI: 10.5220/0004015200240031


in Bibtex Style

@conference{simultech12,
author={Yuri N. Skiba and Denis M. Filatov},
title={Simulation of Shallow-water Flows in Complex Bay-like Domains},
booktitle={Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2012},
pages={24-31},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004015200240031},
isbn={978-989-8565-20-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Simulation of Shallow-water Flows in Complex Bay-like Domains
SN - 978-989-8565-20-4
AU - N. Skiba Y.
AU - M. Filatov D.
PY - 2012
SP - 24
EP - 31
DO - 10.5220/0004015200240031