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Abstract
An improved finite volume algorithm is proposed for modeling the free surface flows. The effects of variable reconstruction and treatments for partially wetted cells on numerical oscillations are demonstrated through a complex field-scale simulation. Results show that the combination of a vertex-based slope limiting approach and an updating strategy that the continuity and momentum equations should be simultaneously updated for partially wetted cells is essential to prevent unphysical oscillations. In this situation, the bed slope terms in wetted cells are exactly discretized, whereas the divergence-form-based approach is adopted for partially wetted cells. This new hybrid method provides an alternative way that precisely preserves the well-balanced property. A practical application of realistic dam-break flood propagation is presented. It is found that the model is free of numerical oscillation and can accurately predict dam-break flows over complicated topography with wetting and drying.
Keywords
Shallow water equations, finite volume algorithm, dam-break floods
Date received: 23 October 2014; accepted: 24 May 2015
Academic Editor: Cheng-Xian Lin
(ProQuest: ... denotes formulae omitted)
Introduction
In recent years, there have been many developments in the field of hydrodynamic numerical modeling. Majority of researchers have focused on the development of various two-dimensional hydrodynamic models, which are based on the depth-averaged shallow water equations and finite volume methods.1-14 In academic and engineering circles, high-performance numerical model for dam-break floods simulation with complex geometry and topography always tends to be a frontier research field. Cao et al.1 developed a new approach based on a two-dimensional full hydrodynamic model for flash flood simulation. Vosoughifar et al.2 employed a high-resolution finite volume method that uses the robust local Lax-Friedrichs scheme for dam-break flood simulation over both wet and dry beds. Begnudelli and Sanders4 detailed a well-designed finite volume algorithm for shallow water flow and scalar transport on triangular grids. The algorithm adopted the Roe-type Riemann solver and monotonic upstream-centered scheme for conservation laws (MUSCL)-Hancock's predictor-corrector scheme. Besides, the proposed volume or free surface relationships (VFRs) provide a robust and mass-conservative way for wetting and drying. Liang6 presented an adaptive quadtree grid-based hydrodynamic model for practical flood simulation. Peng10 adopted the Roeand Harten-Lax-van Leer (HLL)-type finite volume schemes for idealized dam-break flood simulation. Three persistent problems should be taken care when simulating practical dam-break floods: topography...