This solutions manual is a companion to the workbook, Practical Numerical Mathematics with MATLAB: A workbook. It is intended for use by individual students independently studying the workbook and provides complete MATLAB code and numerical results for each of the exercises in the workbook and will be especially useful for those students without previous MATLAB programming experience. It is also valuable for classroom instructors to help pinpoint the author's intent in each exercise and to provide a model for graders.
This monograph aims at presenting a unified approach to numerical modeling of tsunami as long waves based on finite difference methods for 1D, 2D and 3D generation processes, propagation, and runup. Many practical examples give insight into the relationship between long wave physics and numerical solutions and allow readers to quickly pursue and develop specific topics in greater depth. The aim of this book is to start from basics and then continue into applications. This approach should serve well the needs of researchers and students of physics, physical oceanography, ocean/civil engineers, computer science, and emergency management staff. Chapter 2 is particularly valuable as it fully describes the application of finite-difference methods to the study of long waves by demonstrating how physical properties of water waves, especially phase velocity, are connected to the chosen numerical algorithm. Basic notions of numerical methods, i.e. approximation of the relevant differential equations, stability of the numerical scheme, and computational errors are explained through application to long waves. Finite-difference methods are further developed in major chapters to deal with complex problems that arise in the study of recent tsunamis.
Ch. 1. Model for fully nonlinear ocean wave simulations derived using Fourier inversion of integral equations in 3D / J. Grue and D. Fructus -- ch. 2. Two-dimensional direct numerical simulations of the dynamics of rogue waves under wind action / J. Touboul and C. Kharif -- ch. 3. Progress in fully nonlinear potential flow modeling of 3D extreme ocean waves / S.T. Grilli [und weitere] -- ch. 4. Time domain simulation of nonlinear water waves using spectral methods / F. Bonnefoy [und weitere] -- ch. 5. QALE-FEM method and its application to the simulation of free-responses of floating bodies and overturning waves / Q.W. Ma and S. Yan -- ch. 6. Velocity calculation methods in finite element based MEL formulation / V. Sriram, S.A. Sannasiraj and V. Sundar -- ch. 7. High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water / P.A. Madsen and D.R. Fuhrman -- ch. 8. Inter-comparisons of different forms of higher-order Boussinesq equations / Z.L. Zou, K.Z. Fang and Z.B. Liu -- ch. 9. Method of fundamental solutions for fully nonlinear water waves / D.-L. Young, N.-J. Wu and T.-K. Tsay -- ch. 10. Application of the finite volume method to the simulation of nonlinear water waves / D. Greaves -- ch. 11. Developments in multi-fluid finite volume free surface capturing method / D.M. Causon, C.G. Mingham and L. Qian -- ch. 12. Numerical computation methods for strongly nonlinear wave-body interactions / M. Kashiwagi, C. Hu and M. Sueyoshi -- ch. 13. Smoothed particle hydrodynamics for water waves / R.A. Dalrymple [und weitere] -- ch. 14. Modelling nonlinear water waves with RANS and LES SPH models / R. Issa [und weitere] -- ch. 15. MLPG_R method and Its application to various nonlinear water waves / Q.W. Ma -- ch. 16. Large Eddy simulation of the hydrodynamics generated by breaking waves / P. Lubin and J.-P. Caltagirone -- ch. 17. Recent advances in turbulence modeling for unsteady breaking waves / Q. Zhao and S.W. Armfield -- ch. 18. Freak waves and their interaction with ships and offshore structures / G.F. Clauss
Numerical Modeling of Water Waves, Second Edition covers all aspects of this subject, from the basic fluid dynamics and the simplest models to the latest and most complex, including the first-ever description of techniques for modeling wave generation by explosions, projectile impacts, asteroids, and impact landslides. The book comes packaged with a CD-ROM that contains the computer codes and movies generated by the author and his colleagues at the Los Alamos National Laboratory. Mader's three-pronged approach--through text, computer programs, and animations--imparts a thorough understanding of new computational methods and provides the tools to put those methods to effective use.
The tragedy of the 2004 Indian Ocean tsunami has led to a rapid expansion in science directed at understanding tsunami and mitigating their hazard. A remarkable cross-section of this research was presented in the session: Tsunami Generation and Hazard, at the International Union of Geodesy and Geophysics XXIV General Assembly in Perugia, held in July of 2007. Over one hundred presentations were made at this session, spanning topics ranging from paleotsunami research, to nonlinear shallow-water theory, to tsunami hazard and risk assessment. A selection of this work, along with other contributions from leading tsunami scientists, is published in detail in the 28 papers of this special issue of Pure and Applied Geophysics: Tsunami Science Four Years After the Indian Ocean Tsunami. Part I of this issue includes 14 papers covering the state-of-the-art in tsunami modelling and hazard assessment. Another 14 papers are published in Part II focusing on observations and data analysis.
This review volume is divided into two parts. The first part includes five review papers on various numerical models. Pedersen provides a brief but thorough review of the theoretical background for depth-integrated wave equations, which are employed to simulate tsunami runup. LeVeque and George describe high-resolution finite volume methods for solving the nonlinear shallow water equations. The focus of their discussion is on the applications of these methods to tsunami runup.In recent years, several advanced 3D numerical models have been introduced to the field of coastal engineering to calculate breaking waves and wave-structure interactions. These models are still under development and are at different stages of maturity. Rogers and Dalrymple discuss the Smooth Particles Hydrodynamics (SPH) method, which is a meshless method. Wu and Liu present their Large Eddy Simulation (LES) model for simulating the landslide-generated waves. Finally, Frandsen introduces the lattice Boltzmann method with the consideration of a free surface.The second part of the review volume contains the descriptions of the benchmark problems with eleven extended abstracts submitted by the workshop participants. All these papers are compared with their numerical results with benchmark solutions.
Numerical Modeling of Water Waves, Second Edition covers all aspects of this subject, from the basic fluid dynamics and the simplest models to the latest and most complex, including the first-ever description of techniques for modeling wave generation by explosions, projectile impacts, asteroids, and impact landslides. The book comes packaged with
This book introduces a framework of tsunami modelling from generation to propagation, aimed at application to the new observation started in Japan after the devastating tsunami of the 2011 Tohoku-Oki earthquake. About 150 seismic and tsunami sensors were deployed in a wide region off the Pacific coast of eastern Japan in order to catch tsunami generation inside the focal area, which makes a clear departure from conventional observations that detect tsunamis far from the source region. In order to exploit the full potential of this new observation system, it is not enough to model tsunami generation simply by static sea-bottom deformation caused by an earthquake. This book explains dynamic tsunami generation and sea-bottom deformation by kinematic earthquake faulting, in which seismic and acoustic waves are also included in addition to static sea-bottom deformation. It then systematically derives basic tsunami equations from the fundamental equations of motions. The author also illustrates the details of numerical schemes and their applications to tsunami records, making sound linkages among these topics to naturally understand how a tsunami is physically or mathematically described. This book will be a comprehensive guide for graduate students and young researchers to start their research activities smoothly.
Presenting a novel approach to wave theory, this book applies mathematical modeling to the investigation of sea waves. It presents problems, solutions and methods, and explores issues such as statistical properties of sea waves, generation of turbulence, Benjamin-Feir instability and the development of wave fields under the action of wind. Special attention is paid to the processes of dynamic wind-wave interaction, the formation of freak waves, as well as the role that sea waves play in the dynamic ocean/atmosphere system. It presents theoretical results which are followed by a description of the algorithms used in the development of wave forecasting models, and provides illustrations to assist understanding of the various models presented. This book provides an invaluable resource to oceanographers, specialists in fluid dynamics and advanced students interested in investigation of the widely known but poorly investigated phenomenon of sea waves.
This book presents selected articles from the International Conference on Asian and Pacific Coasts (APAC 2019), an event intended to promote academic and technical exchange on coastal related studies, including coastal engineering and coastal environmental problems, among Asian and Pacific countries/regions. APAC is jointly supported by the Chinese Ocean Engineering Society (COES), the Coastal Engineering Committee of the Japan Society of Civil Engineers (JSCE), and the Korean Society of Coastal and Ocean Engineers (KSCOE). APAC is jointly supported by the Chinese Ocean Engineering Society (COES), the Coastal Engineering Committee of the Japan Society of Civil Engineers (JSCE), and the Korean Society of Coastal and Ocean Engineers (KSCOE).
