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Proceedings of the 10th Intl. Conf.on Hydroscience & Engineering, Nov. 4-7, 2012, Orlando, Florida, U.S.A. A STUDY ON SIMULATION OF FLOOD INUNDATION IN A COASTAL URBAN AREA USING A TWO-DIMENSIONAL NUMERICAL MODEL Woochang Jeong1, Jun-Whan Lee2, Yong-Sik Cho3 ABSTRACT In this study, the simulation and analysis for the inundation in a coastal urban area according to the storm surge height are carried out using a two-dimensional numerical model. The target coastal urban area considered in this study is a part of the new town of Changwon city, Gyungnam province, Korea and this area was extremely damaged due to the storm surge generated during the period of the typhoon "Maemi" in September 2003. For the purpose of the verification of the numerical model applied in this study, the simulated results are compared and analyzed with the temporal storm surge heights observed at the tide station in Masan bay and inundation traces in urban areas. Moreover, in order to investigate the influence of super typhoons possible in the future, the results simulated with the storm surge heights increased 1.25 and 1.5 times greater than those observed during the period of the typhoon "Maemi" are compared and analyzed. 1. INTRODUCTION Recent global warming has led to extreme weather conditions, and the 2007 Fourth Assessment Report of United Nations Intergovernmental Panel on Climate Change predicted a temperature rise of up to 6.4oC by the end of the 21st century (IPCC, 2007) and revealed that the sea level would rise by 28~43cm. In Korea, which is surrounded by the sea on three sides, typhoons and storms have frequently caused extensive damages including coastal inundation and erosion, and destruction of coastal structures. These include the No. 14 Typhoon "Sarah" in 1959, No. 5 Typhoon "Thelma" in 1987, No. 15 Typhoon "Rusa" in 2002, and No. 14 Typhoon "Maemi" in 2003, which caused enormous loss of both life and property owing to coastal inundation in areas along the southern coast. The coastal inundation is generated by a combination of various factors, such as seawater level changes due to long period high waves mainly created by tides, storm surges, and tsunamis. The coastal inundation caused by the massive Hurricane "Katrina" in August 2005 brought about enormous damage to the southeast areas of New Orleans in the United States. The property damage (including destruction of houses, harbor bridge facilities, and refinery facilities) was estimated to be 1 Assistant Professor, Department of Civil Engineering, Kyungnam University, Changwon, Korea ([email protected]) 2 Master course's student, Department of Civil and Environmental Engineering, Hanyang University, Seoul, Korea 3 Professor, Department of Civil and Environmental Engineering, Hanyang University, Seoul, Korea, ([email protected]) Proceedings of the 10th Intl. Conf.on Hydroscience & Engineering, Nov. 4-7, 2012, Orlando, Florida, U.S.A. more than $100 billion, the death toll was more than 1,800, and 80% of the city area was submerged because of the failure of the lake floodgates. Typhoon "Winnie", which occurred during the spring tide period on July 15 (according to the lunar calendar) in 1997, caused flood damage in the areas of the west coast, including Mokpo, Sinan, and Muan in Chonnam Province, South Korea, rising the need for systematic investigation into coastal disasters. Therefore, investigations into origins of coastal floods and analyses necessary for establishing comprehensive countermeasures were carried out. Further the enormous damage suffered by Busan and Masan city in Kyungnam Province because of Typhoon "Maemi" in September 2003 also raised social concerns related to storm surges, and theoretical studies on the occurrence of tidal waves and floods and research on the construction of various coastal disaster prevention systems were carried out (Kang, 2004; Choi et al., 2004; Heo et al., 2006a, 2006b; Yi, 2004; Kim et al., 2007). Disasters such as coastal floods are caused by combined factors related to waves and surges. Ozer et al. (2000) attempted to use bi-directional combined models of waves and surges to simulate these phenomena, and Bao et al. (2000) and Cheung et al. (2003) developed a combined model for MM5, POM, WAM, and SWAN to simulate three-dimensional wind structures and ocean currents. Moon and Oh (2003) and Choi et al. (2003) simulated surges caused by typhoons using a combined model that considered interactions between surges, tidal waves, and waves. Recently, using the MIKE 21 model, Mun et al. (2006) simulated and analyzed floods by storm surges in the sea area of Mokpo, and Hur et al. (2008) simulated and analyzed storm surges heights in the coastal areas of Busan and Kyungnam Province in virtual super-storm invasions. The results of their analyses suggested that these storm surge heights may be nearly 1.5~2.0 times higher than the heights that occurred during Typhoon "Maemi", and at least four times higher than the levels that occurred during Hurricane "Katrina". By applying the two-dimensional non-linear shallow water equations to the events of Typhoon "Maemi", they carried out simulations of the flood phenomena caused by storm surges in shore areas. However, most of this research, using storm surge heights observed from tide stations, assumed shores to be impermeable wall structures, estimated only storm surge heights in sea areas, or analyzed only the floodwater occurring in shore areas. Until now, few simulations and researches have focused on the effect on flood inundation of buildings, etc., in coastal urban areas due to storm surges. In this study, the flood inundation in a coastal urban area due to storm surge heights was simulated and analyzed by using the two-dimensional numerical model. The target coastal urban area is a part of new towns of Changwon city which suffered the most extensive damage during Typhoon "Maemi". In order to verify the applied numerical model, we use the storm surge heights recorded during Typhoon "Maemi" and compare the flood traces. Further, in order to investigate the influence of super typhoons that could occur in the future, we compare and analyze the results of flood inundation simulated under the assumed conditions that the storm surge heights increased to 1.25~1.5 times higher than the heights recorded during Typhoon "Maemi". 2. TWO-DIMENSIONAL FINITE VOLUME MODEL 2.1 Governing Equations The governing equations are two-dimensional conserved-type shallow water equations and can be expressed as follows: 2 Proceedings of the 10th Intl. Conf.on Hydroscience & Engineering, Nov. 4-7, 2012, Orlando, Florida, U.S.A. U FUSU (1) t U h,hu,hvT (1a) (1b) where h is the water depth, u and v are the depth-averaged velocities in the x- and y-axis directions, respectively. G(U) and H(U) are the flux vectors in the x- and y-axis directions, respectively. S(U) is the source term, g is the gravity acceleration, and n is the Manning’s roughness coefficient. 2.2 Finite Volume Method with Well-Balanced HLLC Scheme By integrating eq. 1 over an arbitrary cell Ai as shown in Figure 1, the equation of a finite volume method can be written in vector forms as follows: U dA F U ni d S U dA (2) AAAit i i T where F=(E, H) , ∂Ai is the boundary of cell Ai, and ni is the outward unit normal vector to the boundary of cell Ai. Figure 1 Triangular and quadrilateral cells in a two-dimensional unstructured grid system. 3 Proceedings of the 10th Intl. Conf.on Hydroscience & Engineering, Nov. 4-7, 2012, Orlando, Florida, U.S.A. The discretized form of eq. 2 is given for the cell Ai as follows: dU m Ai F U n ij L ij A i S U (3) dt j1 where |Ai| is the surface area of the cell Ai, m is the number of sides of the cell Ai, (m=3 for a triangular cell and m=4 for a quadrilateral cell), Lij is the length of the side j, and nij is the outward unit normal vector from side j. The finite volume method allows directly spatial discretization by introducing the property of the rotational invariance (Toro, 2001). If this property is applied to the flux term in eq. 3, the flux term can be written as follows: F U n T1 G T U (4) ij nij n ij where Tnij is the transformation matrix expressed by Eq. 5. 1 0 0 T 0 cos sin (5) nij ij ij 0 sin ij cos ij By substituting eq. 4 into eq. 5, the following equation can be obtained for the cell Ai. m dUi 1 ATGTU,TULASU (6) i nij ninjijiii ij ij dt j1 where G(TnijUi, TnijUj)=Ğ(UL, UR) is the flux at the boundary of cell Ai and resolved from an approximate solver of the Riemann problem having a left state variable UL and a right state variable UR for cells L and R in Figure 1. Figure 2 Schematic illustration of HLLC flux approximation. In this study, to compute the flux term, the HLLC scheme proposed by Billet and Toro (1997) is employed. This scheme has the first-order accuracy both in time and space and an improved version of the HLL scheme (Harten et al., 1983). Unlike the HLL scheme which considers only two wave 4 Proceedings of the 10th Intl. Conf.on Hydroscience & Engineering, Nov. 4-7, 2012, Orlando, Florida, U.S.A. * speeds SL and SR, the HLLC scheme takes into account the intermediate wave speed S between two wave speeds, as shown in Figure 2. In the HLL scheme, the flux terms in eq.
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