1. m Development of GIS-GPU-based flood-simulation model and its application to flood-risk assessment Computational Engineering and Science for Safety and Environmental Problems 13-16 April 2014 / Sendai International Center, Sendai, Japan Augusto Maidana, Julio García, Eugenio Oñate, Claudio Zinggerling and Miguel A. Celigueta International Center for Numerical Methods in Engineering (CIMNE) Technical University of Catalunya (UPC) Gran Capitán s/n, 08034 Barcelona, Spain maidana@cimne.upc.edu; julio@compassis.com; onate@cimne.upc.edu; czingger@cimne.upc.edu; maceli@cimne.upc.edu, www.cimne.com

2. Outline Introduction – Ideas and motivations – Target application areas – The mathematical model (SWE) – Graphics Processing Units (GPU) Shallow Water Simulations on GPUs – Shallow waters equations – Finite Volume Method – Riemann solver of Roe – Raster approach – Courant-Friedrichs-Lewy condition – Boundary conditions Examples of applications Future works Conclusions

3. Introduction Ideas and motivations : Develop a model to be able adequately simulate the dynamics of gravitatory surface waves to solve problems ranging from the flood wave propagation to the dynamics of tsunami propagating across the continental shelf. Make use of the increasing availability of satellite data in high-resolution images from web pages servers, also of the faster and more powerful computers that incorporate parallel capacity by means the GPUs will allow developing models that make full use of such new datasets as high-resolution digital elevation models (DEMs). The main idea here is to combine the two above points with an Geographic Information Systems software (GIS). This will allow reduced computation times, increased data handling and analysis capability, and improved results and data display. h B hu

4. Floods: Storm Surges: Tsunamis : Dam breaks: Harbor resonance: 2010: Pakistan (2000+) 1931: China floods (2 500 000+) 2005: Hurricane Katrina (1836) 1530: The Netherlands (100 000+) 2011: Japan (5321+) 2004: Indian Ocean (230 000) 1975: Banqiao Dam (230 000+) 1959: Malpasset (423) 2006: Ciutadella harbor, Menorca (Spain) Introduction Target and applications areas :

5. Introduction The mathematical model (SWE) : Shallow Water Equations A hyperbolic partial differential equation First described by Saint-Venant (1797-1886) Gravity-induced fluid motion 2D free surface Negligible vertical acceleration Wave length much larger than depth Conservation of mass and momentum

6. Introduction Graphics Processing Units (GPU): A GPU is faster than a CPU It is possible to get higher quality results in the same timeframe CPUGPU Cores416 Float ops/ clock641024 Frequency (MHz)34001544 GigaFLOPS2171580 Memory (GB)+323

7. Shallow Water Simulations on GPUs Shallow Water Equations (SWE) : Vector of conserved variables Flux Functions Bed slope source term Bed friction source term

8. Shallow Water Simulations on GPUs Finite Volume Discretization (FVM): The grid consists of a set of cells or volumes The bathymetry and the physical variables (h, hu, hv), are piecewise constants per volume The Finite Volume Scheme First order accurate fluxes Well-balanced (captures lake-at-rest) Good match with GPU execution model

9. Shallow Water Simulations on GPUs Riemann solver of Roe:

10. Shallow Water Simulations on GPUs Raster approach: where the flux vector is computed by means de summatory of the four cell sides The equation to homogeneous quadrilateral cells is reduced from the last generalized finite volume scheme Finite volume discretization of a two-dimensional domain with homogeneous quadrilateral cells

11. Shallow Water Simulations on GPUs Courant-Friedrichs-Lewy condition: Explicit scheme, time step restriction: Time step size restricted by Courant-Friedrichs-Lewy condition Each wave is allowed to travel at most 0.9 grid cell per time step: where:

12. Shallow Water Simulations on GPUs Boundary Conditions: NODATA cell:

13. Examples of applications Dam-break on a dry domain without friction (Ritter’s analytical solution): Ritter’s solution of dam-break profiles

14. Examples of applications Dam-break on a dry domain without friction (Ritter’s analytical solution): This solution shows if the scheme is able to locate and treat correctly the wet/dry transition. It also emphasizes whether the scheme preserves the positivity of the water height, as this property is usually violated near the wetting front.

15. Examples of applications Dam-break on a dry domain without friction (Ritter’s analytical solution): Depth at dam side remains constant at 4/9 times of reservoir depth. The classical solutions of Ritter fail to describe accurately the physical flow because of neglecting frictional resistance effects.

16. Examples of applications Ebro River: The main idea to this test is to estimate the celerity of a wave of flooding gliding over a flow base. Figure 1 depicts the flow base employed to estimate the celerity of a flooding wave gliding over the Ebro river in Spain. Figure 2 shows the wave hydrograph between two gauging stations and the processes of translation and attenuation of the wave. D=3748.83 T=3 hr PointsXY P145286 P290294 ∴ D = X2 + Y2 * CellSize = 45.7 cells * 81.87 m = 3748.83 m Wave celerity 3748.83 m3*3600 s=0.347 m/s Bates et al. (1998) report typical values of celerity between 0.3 m s−1 and 1.8 m s−1.

17. Examples of applications Monai Valley: The main idea here was to test the FLOOTSI code to a real-world event, the Okushiri 1993 tsunami, for which laboratory experiments were also performed as part of the set of benchmark problems used in the 2004 Catalina Island workshop (Liu et al., 2008). The laboratory experiments of runup in the Monai Valley were conducted, aimed at reproducing and better understanding the coastal impact of the Okushiri tsunami. This experiment was modeled here as part of a validation benchmark. The laboratory model of Monai at a 1/400 scale was constructed in a 205 m-long, 6 m-deep, and 3.5 m-wide tank at Central Research Institute for Electric Power Industry (CRIEPI) in Abiko, Japan and partly shown in Fig. 1. The laboratory setup closely resembles the actual bathymetry. The incident wave from offshore, at the water depth D = 13.5 cm is known. There are reflective vertical sidewalls at X = 5.5, Y = 0 and 3.5 m (Fig. 1). The entire computational area is 5.448 m x 3.402 m, and the recommended time step and grid sizes for numerical simulations are Cell Size = 1.4 cm and dt = 0.05 sec. Figure 1 depicts the coastal topography of the complex three-dimensional beach. Figure 2 depicts the initial wave profile [ Height(m) - Time(s) ] for Monai Valley experiment.

18. Examples of applications Monai Valley: Figures 3, 4, and 5 depicts the comparison of experimental (Liu et al., 2008) and FLOOTSI’s results for wave gages 1, 2 and 3 for the Catalina benchmark #2 of the Monai Valley. The numerical results reproduce well the salient features of the tsunami-induced flow, particularly for the lower frequency components. The time of initial wave impact and that of arrival of the reflected wave match the experimental values quite well. Figure 3 depicts the comparison between the gage 1 (4.521 m, 1.196 m) and the numerical results of the two nearest points. Figure 4 depicts the comparison between gage 2 (4.521 m, 1.696 m) and the numerical results of the two nearest points. Figure 5 depicts the comparison between the gage 3 (4.521 m, 2.196 m) and the numerical results of the two nearest points.

19. Tool for risk assessment in cases of floods, tsunamis, dam breaks, meteorological tide, etc. Objetives: In preparation for events: Evaluate possible scenarios Creation of inundation maps. Creation of Emergency Action Plans and evacuation. Future works Resilience to natural disasters:

20. Tool for risk assessment in cases of floods, tsunamis, dam breaks, meteorological tide, etc. Objetives: In response to ongoing events: Simulate possible scenarios in real-time. Simulate strategies for flood protection (sand bags, levees, etc.) Determine who to evacuate based on simulation, not guesswork. Future works Resilience to natural disasters:

21. Tool for risk assessment in cases of floods, tsunamis, dam breaks, meteorological tide, etc. Objetives : After the event : Assessment of costs and property damage. Future works Resilience to natural disasters:

22. Conclusions The numerical scheme : Works well for our target scenarios Handles dry zones (land) Handles shocks gracefully (without smearing or causing oscillations) Preserves "lake at rest" Have the accuracy required for capturing the physics Preserves the physical quantities Fits GPUs well Works well with single precision Is embarrassingly parallel Has a compact stencil

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