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Introduction
Published in Quoc VO Thanh, Modeling of Hydrodynamics and Sediment Transport in the Mekong Delta, 2021
This study applies a process-based model which solves the shallow water equations based on the finite volume numerical method (Kernkamp et al., 2011). The Mekong Delta consists of a dense river network, with high variability of channel widths, particularly in the VMD. The river network encompasses natural rivers, man-made canals and floodplains and is a result of water infrastructure development from 1819 onwards (Hung, 2011). Thus a pure 2D model for the entire Mekong Delta is inefficient since it increases the number of computational nodes. Besides, 1D models are efficient in large areas such as the Mekong Delta system, but they are not able to consider the river-sea interaction. The river-sea interaction is very important in sediment transport modeling, as was shown in recent studies (Thanh et al., 2017; Tu et al., 2019; Xing et al., 2017). Therefore, a combination of these two seems a reasonable solution. A hybrid modeling grid which includes 2D cells and 1D elements, is one of optimal and efficient approaches for the Mekong Delta. Moreover, available data of bathymetry of the Mekong River are limited and coarse. This needs a higher resolution of bathymetry data for the 2D cells, so this study introduces a spatial interpolation method for meandering channels, based on the channel-fitted coordinates.
Introduction
Published in Vorawit Meesuk, Point Cloud Data Fusion for Enhancing 2D Urban Flood Modelling, 2017
Even though simulating flow dynamics in more than one direction can be calculated in both 2D and 3D models, simulating these flows in 2D models seem to be more practical and straightforward for most cases of urban flood predictions. In 2D models, an assumption of nearly horizontal flows is indicated in the shallow- water equations, which allow considerable simplifications in mathematical formulations and numerical solutions. This assumption not only considerably simplifies analyses but also yields reasonable explanations and representations. However, vertical flows in 2D models are commonly omitted, but still considerably concerned in 3D models.
Numerical modelling of the intake parts of small hydropower plants
Published in Bjørn Honningsvåg, Grethe Holm Midttømme, Kjell Repp, Kjetil Arne Vaskinn, Trond Westeren, Hydropower in the New Millennium, 2020
A. Drab, J. Jandora, J. Riha, O. Neumayer
The 2D shallow equations are based on the depth averaged flow velocity (depth integration of Navier-Stokes equations). In the study, the steady state approximation with constant turbine inflow discharge and water level position were used. Shallow water equations are frequently used as mathematical model for water flow in coastal areas, lakes, estuaries, etc. These equations can be obtained by integrating the horizontal momentum equations and the continuity equation over the depth a(x,y) = h(x,y) — Zb(x,y). The result of the integration over depth is (Vreugdenhil, 1994), (MIKE 21, 2000): ∂p∂x+∂q∂y=0∂∂x(p2h)+∂∂y(pqh)+ga∂h∂x+cfphp2h2+q2h2−E(∂2p∂x2+∂2q∂y2)=0∂∂y(p2h)+∂∂x(pqh)+ga∂h∂y+cfphp2h2+q2h2−E(∂2p∂x2+∂2q∂y2)=0
Modelling and simulation of pavement drainage
Published in International Journal of Pavement Engineering, 2019
Wolfram Ressel, Anne Wolff, Stefan Alber, Irmgard Rucker
Thus, PSRM (Wolff 2013) has been developed on the basic concept of the non-simplified two-dimensional dynamic wave equation (Shallow Water Equations), which has not been done for the case of pavement runoff before. The Shallow Water Equations consist of a system of partial non-linear differential equations describing the flow of ‘shallow water’, which means that the depth of water is very small compared to the flooded area. This obviously matches with the case of road surface runoff. The assumption that flow velocities and their derivatives in vertical direction are negligible leads to the so-called depth-averaged Shallow Water Equations which consist of one continuity equation and two momentum equations (for the two directions of flow in the two-dimensional approach):