Instability in leapfrog and forward-backward schemes Part II: Numerical simulations of dam break

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Title:	Instability in leapfrog and forward-backward schemes Part II: Numerical simulations of dam break
Authors:	Sun,WY
Contributors:	大氣物理研究所
Keywords:	SHALLOW-WATER EQUATIONS;FINITE-VOLUME METHOD;FLOWS;WAVES
Date:	2011
Issue Date:	2012-03-27 17:30:14 (UTC+8)
Publisher:	國立中央大學
Abstract:	Following Sun's approach [17]. Shuman smoothing instead of conventional diffusion terms is used in a simple two-time step semi-implicit finite volume scheme to simulate dam break. When the Courant number is less than one, the absolute value of amplification factor of the 1D linearized shallow-water equations is 1 in this new scheme. Compared with the characteristic-based semi-Lagrangian schemes and the Riemann solver, this scheme produces excellent results of free water depth and speed of the shock. Numerical simulations show that the water inside the dam initially moves away radially until water almost depletes near the center; then the water moves back to the center and forms a vertical water column there. This paper proves that Shuman smoothing can be used not only in the linearized shallow-water equations discussed in Sun [17] but also in the nonlinear wave equations to control instability around shocks. (C) 2010 Elsevier Ltd. All rights reserved.
Relation:	COMPUTERS & FLUIDS
Appears in Collections:	[Department of Atmospheric Sciences and Graduate Institute of Atmospheric Physics ] journal & Dissertation

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