Streamline Upwind Petrov-Galerkin–Based Shallow Water Model for Large-Scale Geophysical Flows in Cartesian and Spherical Coordinates
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 145, Issue 5
Abstract
The development and implementation of a stabilized finite-element model for the simulation of large-scale geophysical flows using the shallow water equations (SWEs) is presented. The model is derived from the mass and momentum conservative forms of the SWE, with wetting–drying implemented using a front tracking algorithm. Transient hydrodynamic phenomena are resolved using run time h-mesh adaption, such that the initial grid resolution only needs to capture bathymetric features. Cartographic mapping is used to allow the use of Cartesian master elements when the meshing is performed in spherical coordinates. The model is validated using five applications designed to test mass conservation and robustness of the wet–dry scheme, and the cartographic mapping is implemented. The presented finite-element model numerical scheme for large-scale geophysical flows overcomes the limitations of mass conservation that have plagued older finite-element model schemes dependent on the generalized wave continuity equation (GWCE). The presented numerical model derives its novelty from the combination of a mass and momentum conservative finite-element model framework, true wetting–drying, and implicit time stepping with a spatially adaptive mesh and temporally adaptive time integration scheme. To the author’s knowledge, no prior finite-element model works exist with this combination of features in the realm of shallow water simulations for large-scale geophysical flows.
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Acknowledgments
This research was supported by the Environmental Simulator (ES) work package of the USACE’s Engineered Resilient Systems (ERS) and the Flood and Coastal Systems (F&CS) research programs. Information about the ERS program can be found at http://www.erdc.usace.army.mil/Missions/Engineered-Resilient-Systems/, and for the F&CS program it can be found at https://chl.erdc.dren.mil/civil-works/mission-areas/flood-risk-management/.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 145 • Issue 5 • September 2019
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© 2019 American Society of Civil Engineers.
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Received: Jun 11, 2018
Accepted: Jan 24, 2019
Published online: May 24, 2019
Published in print: Sep 1, 2019
Discussion open until: Oct 24, 2019
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