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High-Fidelity Numerical Simulation of Shallow Water Waves

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High-Fidelity Numerical Simulation of Shallow Water Waves High-Fidelity Numerical Simulation of Shallow Water Waves Amir Zainali Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Geosciences Robert Weiss, Chair Scott D. King Jennifer L. Irish Heng Xiao Nina Stark December 2, 2016 Blacksburg, Virginia Keywords: tsunami, dispersive waves, coastal vegetation Copyright 2016, Amir Zainali High-Fidelity Numerical Simulation of Shallow Water Waves Amir Zainali ABSTRACT Tsunamis impose significant threat to human life and coastal infrastructure. The goal of my dissertation is to develop a robust, accurate, and computationally efficient numerical model for quantitative hazard assessment of tsunamis. The length scale of the physical domain of interest ranges from hundreds of kilometers, in the case of landslide-generated tsunamis, to thousands of kilometers, in the case of far-field tsunamis, while the water depth varies from couple of kilometers, in deep ocean, to few centimeters, in the vicinity of shoreline. The large multi-scale computational domain leads to challenging and expensive numerical simulations. I present and compare the numerical results for different important problems | such as tsunami hazard mitigation due to presence of coastal vegetation, boulder dislodgement and displacement by long waves, and tsunamis generated by an asteroid impact | in risk assessment of tsunamis. I employ depth-integrated shallow water equations and Serre-Green-Naghdi equations for solving the problems and compare them to available three- dimensional results obtained by mesh-free smoothed particle hydrodynamics and volume of fluid methods. My results suggest that depth-integrated equations, given the current hardware computational capacities and the large scales of the problems in hand, can produce results as accurate as three-dimensional schemes while being computationally more efficient by at least an order of a magnitude. High-Fidelity Numerical Simulation of Shallow Water Waves Amir Zainali GENERAL AUDIENCE ABSTRACT A tsunami is a series of long waves that can travel for hundreds of kilometers. They can be initiated by an earthquake, a landslide, a volcanic eruption, a meteorological source, or even an asteroid impact. They impose significant threat to human life and coastal infrastructure. This dissertation presents numerical simulations of tsunamis. The length scale of the physical domain of interest ranges from hundreds of kilometers, in the case of landslide-generated tsunamis, to thousands of kilometers, in the case of far-field tsunamis, while the water depth varies from couple of kilometers, in deep ocean, to few centimeters, in the vicinity of shoreline. The large multi-scale computational domain leads to challenging and expensive numerical simulations. I present and compare the numerical results for different important problems | such as tsunami hazard mitigation due to presence of coastal vegetation, boulder dislodgement and displacement by long waves, and tsunamis generated by an asteroid impact | in risk assessment of tsunamis. I employ two-dimensional governing equations for solving the problems and compare them to available three-dimensional results obtained by mesh-free smoothed particle hydrodynamics and volume of fluid methods. My results suggest that two- dimensional equations, given the current hardware computational capacities and the large scales of the problems in hand, can produce results as accurate as three-dimensional schemes while being computationally more efficient by at least an order of a magnitude. Acknowledgments I would like to express my great appreciation to Dr. Robert Weiss, as my adviser, for his guidance, encouragement, and patience during the course of this work. I would also like to thank my dissertation committee members, Drs. Scott King, Jennifer L. Irish, Nina Stark, and Heng Xiao for their helpful comments on the draft of this thesis. I would also like to thank Kannikha Kolandaivelu and Roberto Marivela for reviewing the earlier versions of this dissertation. The work presented in here is based upon work partially supported by the National Science Foundation under Grants No. NSF-CMMI-1208147 and NSF-CMMI-1206271. iv Contents Acknowledgement iv List of Figures ix List of Tables xvii Nomenclature xix 1 Introduction 1 1.1 Theoretical Background . .6 1.2 Contributions and Outline of the Dissertation . 10 2 Boulder Dislodgement and Transport by Solitary Waves: Insights from Three-Dimensional Numerical Simulations† 14 2.1 Introduction . 15 v Contents vi 2.2 Theoretical Background . 17 2.2.1 Governing Equations and Numerical Method . 17 2.2.2 Model Setup . 19 2.2.3 Non-Dimensional Parameters . 20 2.3 Results . 23 2.3.1 Validation of Numerical Results . 23 2.3.2 Boulder Transport by Solitary Waves . 25 2.4 Discussion and Conclusions . 28 3 High-Fidelity Depth-Integrated Numerical Simulations in Comparison to Three-Dimensional Simulations 32 3.1 Introduction . 33 3.1.1 Three-Dimensional Methods . 34 3.1.2 Depth-Integrated Methods . 38 3.2 Results . 39 3.2.1 Non-Breaking Solitary Wave Interaction with a Group of Cylinders . 39 Contents vii 3.2.2 Breaking Solitary Wave Run-Up on a Sloping Beach . 42 3.2.3 Breaking Solitary Type Wave Run-Up on a Sloping Beach . 42 4 Numerical Simulation of Nonlinear Long Waves in the Presence of Discon- tinuous Coastal Vegetation † 45 4.1 Introduction . 46 4.2 Theoretical Background . 49 4.2.1 Initial and Boundary Conditions . 50 4.2.2 Wave Breaking . 51 4.3 Results . 52 4.3.1 Validation of Numerical Results . 52 4.3.2 Breaking Solitary-Type Transient Wave Run-Up in the Presence of Macro-Roughness . 54 4.3.3 Effects of Macro-Roughness on the Local Maximum Local Water Depth 56 4.3.4 Effects of Macro-Roughness on the Local Maximum Momentum Flux . 57 4.3.5 Maximum Run-Up . 58 4.4 Discussion and Conclusion . 61 Contents viii 5 Some Examples for Which Dispersive Effects Can Change the Results Significantly† 64 5.1 Numerical Simulation of Hazard Assessment Generated by Asteroid Impacts on Earth . 65 5.1.1 Numerical Simulation of Tsunami Waves Generated by an Asteroid Explosion near the Ocean Surface . 67 5.1.2 Numerical Simulation of Tsunami Waves Generated by an Asteroid Impact into the Ocean . 69 5.2 Non-Breaking Cnoidal Wave Interaction with Offshore Cylinders . 73 5.3 Hazard Assessment Along the Coastline from the Gaza Strip to the Caesarea, Israel . 76 6 Future Work 79 Bibliography 81 List of Figures 1.1 Location of tsunamis that have happened since 1900 to present day; ( ): caused by a volcanic activity; ( ) caused by a landslide; ( ) caused by an unknown source; ( ) caused by an earthquake. Color codes are as following: dark-red represents the tsunamis that caused more than 1000 casualties or more than 1 billion dollars damage in total; red represents the tsunamis that caused more than 100 casualties or more than 100 million dollars damage in total; orange represents the tsunamis that caused more than 10 casualties or more than 10 million dollars damage in total; yellow represents the tsunamis that caused less than 10 casualties or less than 10 million dollars damage in total . .2 ix List of Figures x 1.2 Histograms of the number of earthquakes versus the death and damage toll. I: less than 10 casualties; II casualties between 10 and 100; III casualties between 100 and 1000; IV casualties between 1000 and 10000; casualties more than 10000. A: damage less than 10 million dollars; B: damage between 10 and 100 million dollars; C: damage between 0.1 and 1 billion dollars; D: damage between 1 and 10 billion dollars; E: damage between 10 and 100 billion dollars; F: damage more than 100 billion dollars; The y-axis is in logarithmic scale. .5 1.3 Casualties and economic loss due to I: unknown source; II: earthquake; III: landslide; IV: volcano; V: meteorological source; The y-axis is in logarithmic scale. .6 1.4 Schematic of a long wave. .7 1.5 Tsunami wave propagation caused by a landslide. The initial ratio between the wavelength and water depth is more than 10. The figure shows the comparison of the three different simulations. (blue) SGN high resolution; (red) SGN low resolution; (green) SWE high resolution. 11 2.1 Sketch of dam-break scenario at t = 0. Water behind the gate starts to flow after sudden gate removal at t = 0. To compare the numerical results with experiments presented by Imamura et al. (2008), we applied: lx = 10 m, ly = 0:45 m, lz = 0:3 m, lxh = 5:5 m, lw = 3 m and hw = 0:15; 0:20; 0:25; 0:3 m. 19 List of Figures xi 2.2 Comparison of numerical and experimental data presented. Experimental −3 data are from Imamura et al. (2008). The case ρb = 1550 kg m is colored in −3 black and case with ρb = 2710 kg m is colored in blue; ( ) experimental results and ( ) SPH simulations. 22 2.3 Time snapshots for scenarios CA, CB and CC with α = 0, (left column) and scenarios CA, CB and CC with α = 1, (right column) with wave height of 0:15m. Please note that different cases are superimposed on the same domain just for illustration purposes. 24 2.4 Contour plots of boulder maximum displacement, db, as a function of non- dimensional parameters. a: aspect ratio in logarithmic scale versus Froude number; (a-1) β = −8~30 (a-2) β = 0 and (a-3) β = 4~30. b: submergence factor versus Froude number; (b-1) α = −1, (b-2) α = 0 and (b-3) α = 1. c: submergence factor versus aspect ratio in logarithmic scale; (c-1) F r = 1:08, (c-2) F r = 1:15 and (c-3) F r = 1:22. White regions indicate no significant −1 boulder movement, i.e.
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