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1. 1 AREAS OF APPLICATION FOR THE SHALLOW WATER EQUATIONS The shallow water equations describe conservation of mass and mo mentum in a fluid. They may be expressed in the primitive equation form Continuity Equation _ a, + V. (Hv) = 0 L(l;,v;h) at (1. 1) Non-Conservative Momentum Equations a M("vjt,f,g,h,A) = at(v) + (v. V)v + tv - fkxv + gV, - AIH = 0 (1. 2) 2 where is elevation above a datum (L) ~ h is bathymetry (L) H = h + C is total fluid depth (L) v is vertically averaged fluid velocity in eastward direction (x) and northward direction (y) (LIT) t is the non-linear friction coefficient (liT) f is the Coriolis parameter (liT) is acceleration due to gravity (L/T2) g A is atmospheric (wind) forcing in eastward direction (x) and northward direction (y) (L2/T2) v is the gradient operator (IlL) k is a unit vector in the vertical direction (1) x is positive eastward (L) is positive northward (L) Y t is time (T) These Non-Conservative Momentum Equations may be compared to the Conservative Momentum Equations (2. 4). The latter originate directly from a vertical integration of a momentum balance over a fluid ele ment. The former are obtained indirectly, through subtraction of the continuity equation from the latter. Equations (1. 1) and (1. 2) are valid under the following assumptions: 1. The fluid is well-mixed vertically with a hydrostatic pressure gradient. 2. The density of the fluid is constant.
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The first edition of Handbook of Human Factors and Ergonomics in Health Care and Patient Safety took the medical and ergonomics communities by storm with in-depth coverage of human factors and ergonomics research, concepts, theories, models, methods, and interventions and how they can be applied in health care. Other books focus on particular human factors and ergonomics issues such as human error or design of medical devices or a specific application such as emergency medicine. This book draws on both areas to provide a compendium of human factors and ergonomics issues relevant to health care and patient safety. The second edition takes a more practical approach with coverage of methods, interventions, and applications and a greater range of domains such as medication safety, surgery, anesthesia, and infection prevention. New topics include: work schedules error recovery telemedicine workflow analysis simulation health information technology development and design patient safety management Reflecting developments and advances in the five years since the first edition, the book explores medical technology and telemedicine and puts a special emphasis on the contributions of human factors and ergonomics to the improvement of patient safety and quality of care. In order to take patient safety to the next level, collaboration between human factors professionals and health care providers must occur. This book brings both groups closer to achieving that goal.
Free-Surface Flow: Computational Methods presents a detailed analysis of numerical schemes for shallow-water waves. It includes practical applications for the numerical simulation of flow and transport in rivers and estuaries, the dam-break problem and overland flow. Closure models for turbulence, such as Reynolds-Averaged Navier-Stokes and Large Eddy Simulation are presented, coupling the aforementioned surface tracking techniques with environmental fluid dynamics. While many computer programs can solve the partial differential equations describing the dynamics of fluids, many are not capable of including free surfaces in their simulations. - Provides numerical solutions of the turbulent Navier-Stokes equations in three space dimensions - Includes closure models for turbulence, such as Reynolds-Averaged Navier-Stokes, and Large Eddy Simulation - Practical applications are presented for the numerical simulation of flow and transport in rivers and estuaries, the dam-break problem and overland flow
This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean
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Covering a wide range of techniques, this book describes methods for the solution of partial differential equations which govern wave propagation and are used in modeling atmospheric and oceanic flows. The presentation establishes a concrete link between theory and practice.
Beginning with the development of finite difference equations, and leading to the complete FDTD algorithm, this is a coherent introduction to the FDTD method (the method of choice for modeling Maxwell's equations). It provides students and professional engineers with everything they need to know to begin writing FDTD simulations from scratch and to develop a thorough understanding of the inner workings of commercial FDTD software. Stability, numerical dispersion, sources and boundary conditions are all discussed in detail, as are dispersive and anisotropic materials. A comparative introduction of the finite volume and finite element methods is also provided. All concepts are introduced from first principles, so no prior modeling experience is required, and they are made easier to understand through numerous illustrative examples and the inclusion of both intuitive explanations and mathematical derivations.