1 INTRODUCTION

The standard practice for simulating realistic flood events is the application of numerical models based on solving the 1-D, 2-D or hybrid 1-D/2-D shallow water (Saint-Venant) equations. The use of 1-D codes is highly popular since they are able to com-pute flood events in natural environments in large domains in a relatively short amount of time and us-ing readily available computing resources. 1-D codes assume the flow is essentially unidirectional making them incapable of simulating lateral diffu-sion of flood waves into the floodplain (Hunter, et al 2007). 2-D codes overcome these limitations by solving the 2-D Saint Venant equations, which are obtained by depth-averaging the Navier-Stokes equations. The main limitations of the 2-D Saint Venant equations arise from the derivation of the equations, in which hydrostatic pressure distribution is assumed over the vertical direction. It is because of these limitations that 2-D codes are unable to ac-curately predict mean flow and turbulence in regions where the flow is highly 3D and non-isotropic (flows with separation, flow around hydraulic struc-tures, river confluences, etc.). It is well documented that the flow field increases its level of three dimen-sionality during unsteady events such as floods, es-pecially in regions of high stream curvature, around hydraulic structures and in the transition region be-tween main channel and floodplain. These flow complexities make a strong case for the use of a 3-D

non-hydrostatic Navier Stokes model with de-formable free-surface capabilities to simulate un-steady flood wave propagation in the domain. Such models should be able to offer a better representa-tion of the mean flow field across the domain. By simulating exactly the same test case using the 3-D and the 2-D model, one can get a better idea about the accuracy of the latter model. This is important, given the lack of extended validation data for flood predictions.

A critical assessment of the performance of standard 2D flood models based on results of 3D URANS simulations

D.V. Horna Munoz

IIHR-Hydroscience and Engineering, The University of Iowa, Iowa City, Iowa, United States of America

ABSTRACT: Evaluating the accuracy of 2D depth-averaged solvers to predict flood propagation in natural environments is one of the most important challenges to mitigate floods. This paper discusses the perfor-mance of SRH-2D, a standard 2D flood propagation solver in terms of predicted flood extent and depth-aver-aged velocity profiles in a complex bathymetry river reach for high flow conditions. The accuracy of the 2D solver is mainly evaluated based on comparison with results obtained using a 3D URANS two-phase flow model developed using the commercial software STAR-CCM+. The 2D model performance is evaluated for a steady-state test case. The domain contains a 7-km reach of the Iowa River near Iowa City and 2 river dams. Even though the SRH-2D depth-averaged velocities show the same pattern as the 3D depth-averaged results, the 2D model tends to underpredict the location and magnitude of the peak unit discharge inside the channel, especially in the regions where 3D effects are significant.

In the present paper, we report a case study in which the flood extent and depth-averaged velocity profiles were obtained in a 6-km reach of the Iowa

River near Iowa City (Iowa, United States of Amer-ica) for steady state under high flow conditions. The reach contains two dams (Fig. 1). The bathymetry and topography information were provided by the Iowa Flood Center. Results obtained using SRH-2D, a standard 2-D depth-averaged shallow flow solver, are compared to those obtained with STAR-CCM+, a 3-D non-hydrostatic viscous solver using the k-ε turbulence model and a deformable free-surface module based on the Volume-of-Fluid (VOF) method. A mesh with 6 million cells was used in 3D simulation. SRH-2D solves the full 2-D Shallow Water equations with a parabolic turbulence model. Roughness parametrization was accounted by speci-fying regions with different values of Manning’s co-efficient across the domain.

Figure 1. Close-up view showing the start of computational do-main (1’-1’), the end of the computational domain (2’-2’), the location of the first river dam (2-2) and the location of the sec-ond river dam (3-3).

2 RESULTS

Based on comparison with USGS gage at the only location where stage was measured, the results ob-tained with the calibrated SRH-2D model overesti-mate the free-surface elevation by approximately 1 ft (30 cm) while STAR-CCM+ underestimate the mea-sured data. It is important to mention that while SRH-2D had to be calibrated for low and high flow conditions, STAR-CCM+ results were obtained with no calibration. At steady state, the difference in flood extent area is approximately 21% with respect to the results obtained with STAR-CCM+. Flood ex-

tents for STAR-CCM+ (3D) and SRH-2D (2D) are shown in Figure 2 and 3 respectively.

Qualitatively, there is little difference between the flood extents. The most noticeable difference is ob-served near the area between cross-sections 1 and 2, in which SRH-2D inundates a significant amount of area more compared to STAR-CCM+. Areas close to cross-sections 7 and 8 also show a slight differ-ence between the 2 solutions.

The full paper contains a detailed comparison be-tween the unit-discharge profiles in representative cross-sections between the 2D and 3D models. The comparison will show that several regions are present where fairly significant differences occur be-tween the two models. They generally happen in re-gions where the degree of flow three-dimensionality is high (e.g., regions of high channel curvature, re-gions containing large-scale deformations at the bed).

3 CONCLUSIONS AND FUTURE WORK

The results reported in this paper suggests that the predictive capabilities of 2D solvers used to model flood propagation can decay significantly in regions where 3D effects are important. Future research plans include performing an unsteady simulation in the same river reach to assess the performance of the 2D model during a fast extreme flood event.

Figure 2. Aerial view of flood extent for results obtained with STAR-CCM+

Figure 3. Aerial view of flood extent for results obtained with SRH-2D

REFERENCES

Frank, E. A., Ostan, A., Coccato, M., and Stelling, G. S. “Use of an integrated one dimensional/two dimensional hydraulic modeling approach for flood hazard and risk mapping” In River Basin Management, by R. A. Falconer and W. R. Blain, 99-108. Southhampton, UK: WIT Press, 2001

Hunter, N. M., Bates, P., Horrit, M., Wilson, M. (2007) “Sim-ple spatially-distributed models for predicting flood inunda-tion: A review” Geomorphology: 208-225