Simulation of flow in compound open-channel using a discontinuous Galerkin finite-element method with Smagorinsky turbulence closure

Numerical simulation of hydrodynamic characteristics and bedload transport in cross sections of two gravel-bed rivers based on one-dimensional lateral distribution method

“…5a) in which the model-predicted bed shear stress overestimates the observed data. Previous studies (Knight et al, 1990;Pham Van et al, 2014) showed that the bed shear stress can increase sufficiently due to the effects of bed-generated turbulence when the depth of water in the river cross section is low, which may account for the overestimation of the modelpredicted bed shear stress for low flow conditions.…”

“…The eddy viscosity can be calculated by using different options such as a constant value, zero-equation, one-equation, two-equation, and the Smagorinsky turbulence models (Pham Van et al, 2014). In the current study, the zero-equation turbulence model is selected to compute the eddy viscosity, because in the framework of depth-averaged, uniform, openchannel flow models no significant advantage may be obtained by using more complicated models such as one-and two-equation turbulence models (Pham Van et al, 2014;Vionnet et al, 2004). The zero-equation turbulence model is given as:…”

“…Then, Equation 1 is solved numerically by using a finite difference method, resulting in a discrete equation that is solved with the Newton-Raphson iteration method (Ben-Israel, 1966). The free slip condition also is applied at the river banks because the influence of the river banks is limited to the region close to the banks (Pham Van et al, 2014). Next, the bedload transport rate and bedload transport discharge are computed in the bedload transport module, in which the nondimensional sediment transport rate is calculated using the six formulae.…”

“…Local flow velocity, which is a key hydraulic characteristic in a river cross section, often varies significantly in space due to various factors, e.g., local topography and the transverse transfer of momentum between fast flow in deep areas and adjacent slower flow in shallow areas of the cross section (Pham Van et al, 2014;Sellin, 1964). Observed data and field measurements using an acoustic Doppler current profiler (Dinehart & Burau, 2005) as well as three-dimensional numerical model results (Riesterer et al, 2016) also show that the effects of (lateral) secondary flow on the local flow velocity are significant because of the influence of non-uniformity of velocity caused by bed friction effects and local topography, even in straight channels (Bousmar & Zech, 2001;Ervine et al, 2000;Knight et al, 1994).…”

Floodwater impacts on residential areas in floodplain areas along Day River system in emergency situation

“…This coefficient for local flow structures is used in one of the most celebrated subgrid-scale models for eddy viscosity proposed by Smagorinsky (1963). The Smagorinsky turbulent model allows a better presentation of non-uniform velocity in a floodplain and in transition regions between plain and main channels (Lin et al, 2008;Ahmadi et al, 2009;Pham Van et al, 2014). Many studies have utilized the coefficient of eddy viscosity from the Smagorinsky model in calculations of complex turbulent flows (Tejada-Martínez et al, 2009;Rakowsky et al, 2013;Chacón Rebollo et al, 2014;Werren et al, 2016;Marras et al, 2018).…”