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February 2007.
Spectral methods have a long history of application to fluid flow simulations. Their main advantages are high-order accuracy and convergence properties. The basic spectral methods only work on rectangular or circular domains. A very important and active research area is to adapt spectral methods for domains with complex boundary. In this monograph the application of pseudospectral (PS) method to viscous flow over a two-dimensional cylinder with dimples on the boundary is presented. By using a series of coordinate transformations, the exterior domain is mapped to the interior of the unit disk. Then the Fourier-Chebyshev PS approximation is applied to the transformed system of partial differential equations. Both steady and unsteady solutions are discussed. This monograph should be useful to applied mathematicians and engineers interested in high-order methods for fluid flow simulations in irregular domains.
Pseudospectral method -- Navier-Stokes equations.
The LES-method is rapidly developing in many practical applications in engineering The mathematical background is presented here for the first time in book form by one of the leaders in the field
The field of Large Eddy Simulations is reaching a level of maturity that brings this approach to the mainstream of engineering computations, while it opens opportunities and challenges. The main objective of this volume is to bring together leading experts in presenting the state-of-the-art and emerging approaches for treating complex effects in LES. A common theme throughout is the role of LES in the context of multiscale modeling and simulation.
Numerical Modelling of Wave Energy Converters: State-of-the Art Techniques for Single WEC and Converter Arrays presents all the information and techniques required for the numerical modelling of a wave energy converter together with a comparative review of the different available techniques. The authors provide clear details on the subject and guidance on its use for WEC design, covering topics such as boundary element methods, frequency domain models, spectral domain models, time domain models, non linear potential flow models, CFD models, semi analytical models, phase resolving wave propagation models, phase averaging wave propagation models, parametric design and control optimization, mean annual energy yield, hydrodynamic loads assessment, and environmental impact assessment. Each chapter starts by defining the fundamental principles underlying the numerical modelling technique and finishes with a discussion of the technique’s limitations and a summary of the main points in the chapter. The contents of the chapters are not limited to a description of the mathematics, but also include details and discussion of the current available tools, examples available in the literature, and verification, validation, and computational requirements. In this way, the key points of each modelling technique can be identified without having to get deeply involved in the mathematical representation that is at the core of each chapter. The book is separated into four parts. The first two parts deal with modelling single wave energy converters; the third part considers the modelling of arrays; and the final part looks at the application of the different modelling techniques to the four most common uses of numerical models. It is ideal for graduate engineers and scientists interested in numerical modelling of wave energy converters, and decision-makers who must review different modelling techniques and assess their suitability and output. Consolidates in one volume information and techniques for the numerical modelling of wave energy converters and converter arrays, which has, up until now, been spread around multiple academic journals and conference proceedings making it difficult to access Presents a comparative review of the different numerical modelling techniques applied to wave energy converters, discussing their limitations, current available tools, examples, and verification, validation, and computational requirements Includes practical examples and simulations available for download at the book’s companion website Identifies key points of each modelling technique without getting deeply involved in the mathematical representation
This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flow, in clear and elementary terms. With many examples throughout, the work will be useful to those teaching at the graduate level, as well as to researchers working in the area.
Advanced Engineering Mathematics: Applications Guide is a text that bridges the gap between formal and abstract mathematics, and applied engineering in a meaningful way to aid and motivate engineering students in learning how advanced mathematics is of practical importance in engineering. The strength of this guide lies in modeling applied engineering problems. First-order and second-order ordinary differential equations (ODEs) are approached in a classical sense so that students understand the key parameters and their effect on system behavior. The book is intended for undergraduates with a good working knowledge of calculus and linear algebra who are ready to use Computer Algebra Systems (CAS) to find solutions expeditiously. This guide can be used as a stand-alone for a course in Applied Engineering Mathematics, as well as a complement to Kreyszig’s Advanced Engineering Mathematics or any other standard text.