# Numerical Study of Partial Dam-Break Flow with Arbitrary Dam Gate Location Using VOF Method
## 1 Introduction  
The problem of concrete dam-break is a crucial issue in many countries, causing huge potential risks, as well as having devastating consequences on downstream valleys. This topic has been of significant research interest, receiving both practical and academic attention in recent decades. In application, precise calculation of dam-break floods for complicated types of rapid flows provides for necessary mitigation of, or prevention of, terrible hazards at floodplain areas [1, 2, 3, 4, 5]. Hydraulic information concerning dam-break propagation waves is very useful when building early-warning scenarios at downstream areas [6, 7, 8]. Experimental studies of total and partial dam-break problems have mainly focused on measurements of temporal variation in flow depth, velocity, pressure and outflow hydrographs [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. A limited amount of physical modeling measures other hydraulic features, like hydrodynamic force or flood mappings [4, 16]. However, due to fast-moving flood waves and limitation of measuring devices, observed data may not cover all hydraulic phenomena occurring in the entire physical model. Actually, Computational Fluid Dynamics (CFD) is applied to a wide range of research and engineering problems, including aerodynamics and aerospace analysis, natural science and environmental engineering, industrial system design and analysis, biological engineering, fluid flows and heat transfer, etc. [13, 14, 15] Numerical studies of partial dam-break flow have been primarily conducted by means of several mathematical models. In recent decades, the 2D shallow water equations (SWE) method has been widely used insimulating rapid flow [1; 2; 3; 17; 18; 19; 20; 21]. 2D SWEs can investigate the following typical hydraulic characteristics: profiles of water depth, velocity components, and discharge hydrographs of discontinuous flow. The robustness and effectiveness of 2D mathematical modeling in simulating free surface flow over complex geometry and topography has been proved in much literature [1; 2; 3; 18; 19; 20; 21]. Despite their usefulness in dam-break problems, SWEs do not sufficiently capture some hydraulic phenomena, especially those in the near-field, because this method assumes the disregarding of vertical acceleration and hydrostatic pressure [20; 23]. Due to the highly transient nature of dam-break flow, it is quite difficult to precisely conduct 3D flows of partial dam failure by means of a 2D mathematical method. The absence of turbulent terms in 2D SWEs leads to the methods not capturing the occurrence of turbulence or vortexes in dam-break flow [21; 22]. With an increase in computer processing power, the volume of fluid (VOF) advection algorithm, coupled with Navier-Stokes governing equations, has gained popularity to solve dam-break problems. Indeed, dam-break flow locally has a three-dimensional nature in near-field and wave disturbances occurring downstream. High-resolution numerical modeling can provide useful, advanced information at those positions [18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28]. Most of the modeling concentrates on studying shock wave propagation at floodplain areas [20; 28]. There are only a few researchers who have provided information on return flow occurring in reservoirs. Sophisticated hydraulic features, such as streamline, vorticity, and q-criterion, have rarely been focused on in previous studies. Therefore, in this primary study, we use a 3D hydrodynamic model to investigate the dynamic and structure of flow field within reservoirs regarding different initial water stages, breach sizes and dam gate locations. In general, the maximum flow rate at dam site is the most important feature in predicting flood hazards downstream [6; 11; 12; 29; 30; 31; 32]. Major researchers investigate this information as a function of alternative parameters of the reservoir, including the shape of cross section, geometry of bathymetry, or initial condition of water level, by means of physical models or analytical methods.