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Two-dimensional simulation of shallow-water waves by Lagrangian block advection

Tan, Lai Wai and Chu, Vincent H. (2012) Two-dimensional simulation of shallow-water waves by Lagrangian block advection. Computers and Fluids, 65. pp. 35-43. ISSN 0045-7930

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Abstract

Waves in shallow water are computed by moving blocks of water in the direction of the flow using a Lagrangian method. The mass and momentum in the displaced-and-deformed blocks after the Lagrangian advection are re-distributed back on to the Eulerian mesh to form new blocks at every increment of time. This Lagrangian block advection guarantees for positive water depth. It also prevents the occurrence of unphysical numerical oscillations. Several numerically challenging problems are considered in a series of simulations using the method. The first problem is the tracking of wetting-and-drying interface in a parabolic bowl. The second problem is the capture of depth and velocity discontinuities across the shock waves. Finally, the block advection method is applied to calculate the flood waves overtopping a meandering river. The results of the simulations are compared with the exact solutions. The convergence of Lagrangian block advection towards the exact solutions is first-order accurate in the simulations of the depth-and-velocity discontinuities.

Item Type: Article
Uncontrolled Keywords: lagrangian method; block advection; shallow-water waves; capturing shock waves; tracking wetting-and-drying interface; positivity of water depth; discontinuous solutions
Subjects: T Technology > TC Hydraulic engineering. Ocean engineering
Divisions: Faculty of Civil and Environmental Engineering > Department of Water and Environmental Engineering
Depositing User: Normajihan Abd. Rahman
Date Deposited: 28 May 2013 02:55
Last Modified: 22 Jan 2015 00:16
URI: http://eprints.uthm.edu.my/id/eprint/3922
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