Finite-Volume and Shock-Capturing Shallow Water Equation Model to Simulate Boussinesq-Type Lock-Exchange Flows
Publication: Journal of Hydraulic Engineering
Volume 139, Issue 12
Abstract
Among the various applications of the shallow water equations (SWEs) is the simulation of gravity currents (GCs). The SWEs are used as an alternative to track GC motion without explicitly dealing with turbulent processes, and constitute an intermediate solution between simpler integral models and more comprehensive models based on the Navier-Stokes equations. While the SWE equations have been successfully applied to a number of problems involving the release of dense fluids into deep ambient conditions, a more complex application is the simulation of the lock-exchange problem. In this particular problem, the ambient velocity influences the velocity as well as the shape of the GC, especially in the initial slumping stage. Features resembling discontinuities between the two layers are generated, and one numerical solution strategy has been to explicitly track such discontinuities. This work presents a shock-capturing, two-layer SWE model to simulate lock-exchange flows and its discontinuities. The main contributions are a reformulated mathematical model that incorporates the upper layer effects to the GC flow as well as a more efficient numerical solution for the flow at the GC front. The resulting numerical model was implemented using the finite-volume method (FVM) with an approximate Riemann solver, and the results compare well to existing numerical models as well as experimental data collected during this investigation.
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Acknowledgments
The authors are grateful for the financial support to conduct this investigation provided by the Marine Environmental Sciences Consortium (MESC-TASK ORDER T2-006-AU).
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Published In
Journal of Hydraulic Engineering
Volume 139 • Issue 12 • December 2013
Pages: 1223 - 1233
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jul 20, 2012
Accepted: May 8, 2013
Published online: May 11, 2013
Discussion open until: Oct 11, 2013
Published in print: Dec 1, 2013
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