HYDRODYNAMIC MODELING

water depth, velocity, and the extent of inundation of a flooding event, all of which are very important in flood risk analysis. Flows for which flood water depth and velocity vary, not only with location in space but also with time, are considered as transient or unsteady flow. In rivers and floodplains, flows can be considered as steady for the purposes of an approximate representation of overland flooding in time and location in space. However, for more accurate modeling, the analysis of overland flooding requires considering the flow as unsteady or transient. In 1871, Barrède Saint-Venant formulated the basic theory that considered the analysis of unsteady flow through the coupling of the continuity and momentum equations. Modeling of fluid flow is possible either as one- dimensional, where the direction of flow is predetermined and thereby making approximation or as two-dimensional, where the direction of flow is not predetermined, and is therefore not restricted.

The hydrodynamic modeling used in this research is presented as a powerful tool for addressing river and urban flooding and also for modeling spatial and temporal variability in flood water level, discharge, velocity, etc. Flow in rivers and through pipes can be accurately modeled considering one-dimensional representation. However, consideration of one-dimensional representation will not accurately model overland flooding. Therefore the flow should be considered as unsteady or transient while modeling overland flooding in two-dimensions. Since an analytical solution of the Saint-Venant equations is not possible, the complete Saint-Venant equations must be solved numerically for overland flooding. The most common numerical solutions to the Saint-Venant equations are the finite element and finite difference methods.

There are a number of studies that compare one-dimensional (1-D) and two-dimensional (2-D) approaches in river flood modeling (Horritt and Bates, 2002; Lin et. al., 2006). In confined channels, such as pipe networks, the 1D sewer model can provide acceptable results as long as the water is contained within the street network (Mark et. al., 2004). If the water overflows the curbs and flows overland, the flow may change direction. Under these circumstances the 1D model should not be used, and the 2D model becomes the preferred choice. Leandro, et al. (2009) also concluded that 1D models can provide an adequate approximation of flow in confined channels (such as rivers, pipes and streets), however 2D models give better results for the flow over terrain. Early urban hydrologic models did not have the capability to model the excess flow from the manholes as overland flooding. The surcharged flow remained atop of the manholes until the capacity of the sewer networks was at a maximum. When sewer network capacity became available, the excess water was allowed to drain back into the storm sewer network (Rossman, 2005; Zhong, 1998). This shortcoming in the earlier storm sewer models was overcome by introducing links between surface networks and pipe networks (Leandro et al., 2009).

The use of hydrodynamic modeling in river and urban flooding is becoming very common as the result of: (i) the time needed for the numerical modeling of full Saint Venant equations has become more acceptable, (ii) an increased availability of high resolution topographic data, such as LIDAR, which is required as input into the 2D hydrodynamic model, and (iii) the accumulation of more detailed and accurate results of water level, velocity, discharge etc that are essential for effective river and urban flood

investigation (Smith, et. al., 2006).

Some examples of the commercial tools used for 1D river modeling are HEC-RAS (Hydraulic Engineering Center, 2010), MIKE 11 (DHI, 2008,(a)) and SOBEK (WL|Delft Hydraulics, 2005). For 1D pipe flow modeling, examples include MOUSE (DHI, 2004), MIKE URBAN (DHI, 2009), XP-SWMM (XP Software, 2010), EPA SWMM (EPA, 1995) and PC-SWMM (CHI, 2006). For 2D overland flow modeling examples include MIKE 21 (DHI, 2008,(b)), TUFLOW (Phillips et. al., 2005), SOBEK, GSSHA (Charles et. al., 2006), RMA2 (Barbara et. al., 2006). The commercial hydraulic/hydrodynamic models, such as MIKE URBAN (DHI, 2009) or Infoworks CS (Wallingford Software, 2006) have the capability to model the dynamic interactions between surface networks and pipe/sewer networks by using a weir or an orifice equation (Kawaike and Nakagawa, 2007; Mark et al., 2004; Nasello and Tucciarelli, 2005, Leandro et. al., 2007). Recently there has been a growing trend towards integrating two or more hydrodynamic models to overcome the weakness in linkage between two models. Examples of such models are (1D/2D) MOUSE-MIKE21, which couples the 1D MOUSE pipe/sewer model with the 2D MIKE21 overland model (Carr and Smith, 2006); the (1D/2D) SOBEK Urban, which couples the 1D SOBEK flow with 2D Delft FLS (Bolle et al., 2006); or TUFLOW. The current trend in river flood modeling is to couple a 1D river model with a 2D overland/surface flow model, and in the case of urban flood modeling, a 1D pipe flow model is coupled with a 2D overland flow model. In certain cases all of the three models – (i) 1D river model, (ii) pipe flow model, and (iii) overland flow model – may be coupled together. Researchers have attempted to compare the 1D/1D and 1D/2D couple

models (Kaushik, 2006; Chen et al., 2007). More recently, Leandro, et. al. (2009) provided a comparison between a 1D sewer model coupled with a 1D surface network model (1D/1D) and a 1D sewer model coupled with a 2D overland/surface flow model (1D/2D).

There are certain limitations in 2D hydrodynamic modeling, such as computation time, requirement of more data, etc. The computation time in 2D modeling is significantly higher compared to 1D modeling (Paquier et al., 2003; Lhomme et al., 2006). However, it should be noted that the 1D hydrodynamic model does not provide satisfactory results for solving overland flow, in which case 2D hydrodynamic modeling is required.