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Covers the theory and applications of using weak form theory in incompressible fluid-thermal sciences Giving you a solid foundation on the Galerkin finite-element method (FEM), this book promotes the use of optimal modified continuous Galerkin weak form theory to generate discrete approximate solutions to incompressible-thermal Navier-Stokes equations. The book covers the topic comprehensively by introducing formulations, theory and implementation of FEM and various flow formulations. The author first introduces concepts, terminology and methodology related to the topic before covering topics including aerodynamics; the Navier-Stokes Equations; vector field theory implementations and large eddy simulation formulations. Introduces and addresses many different flow models (Navier-Stokes, full-potential, potential, compressible/incompressible) from a unified perspective Focuses on Galerkin methods for CFD beneficial for engineering graduate students and engineering professionals Accompanied by a website with sample applications of the algorithms and example problems and solutions This approach is useful for graduate students in various engineering fields and as well as professional engineers.
Covers the theory and applications of using weak form theory in incompressible fluid-thermal sciences Giving you a solid foundation on the Galerkin finite-element method (FEM), this book promotes the use of optimal modified continuous Galerkin weak form theory to generate discrete approximate solutions to incompressible-thermal Navier-Stokes equations. The book covers the topic comprehensively by introducing formulations, theory and implementation of FEM and various flow formulations. The author first introduces concepts, terminology and methodology related to the topic before covering topics including aerodynamics; the Navier-Stokes Equations; vector field theory implementations and large eddy simulation formulations. Introduces and addresses many different flow models (Navier-Stokes, full-potential, potential, compressible/incompressible) from a unified perspective Focuses on Galerkin methods for CFD beneficial for engineering graduate students and engineering professionals Accompanied by a website with sample applications of the algorithms and example problems and solutions This approach is useful for graduate students in various engineering fields and as well as professional engineers.
Approaches computational engineering sciences from the perspective of engineering applications Uniting theory with hands-on computer practice, this book gives readers a firm appreciation of the error mechanisms and control that underlie discrete approximation implementations in the engineering sciences. Key features: Illustrative examples include heat conduction, structural mechanics, mechanical vibrations, heat transfer with convection and radiation, fluid mechanics and heat and mass transport Takes a cross-discipline continuum mechanics viewpoint Includes Matlab toolbox and .m data files on a companion website, immediately enabling hands-on computing in all covered disciplines Website also features eight topical lectures from the author’s own academic courses It provides a holistic view of the topic from covering the different engineering problems that can be solved using finite element to how each particular method can be implemented on a computer. Computational aspects of the method are provided on a companion website facilitating engineering implementation in an easy way.
Handbook of Fluid Dynamics offers balanced coverage of the three traditional areas of fluid dynamics—theoretical, computational, and experimental—complete with valuable appendices presenting the mathematics of fluid dynamics, tables of dimensionless numbers, and tables of the properties of gases and vapors. Each chapter introduces a different fluid dynamics topic, discusses the pertinent issues, outlines proven techniques for addressing those issues, and supplies useful references for further research. Covering all major aspects of classical and modern fluid dynamics, this fully updated Second Edition: Reflects the latest fluid dynamics research and engineering applications Includes new sections on emerging fields, most notably micro- and nanofluidics Surveys the range of numerical and computational methods used in fluid dynamics analysis and design Expands the scope of a number of contemporary topics by incorporating new experimental methods, more numerical approaches, and additional areas for the application of fluid dynamics Handbook of Fluid Dynamics, Second Edition provides an indispensable resource for professionals entering the field of fluid dynamics. The book also enables experts specialized in areas outside fluid dynamics to become familiar with the field.
A theory is developed in one and two space dimensions that successfully predicts optimal algorithm constructions for the convection operator intrinsic to unsteady Navier-Stokes (NS) problem statements. The analysis statement is parameterized via a Taylor series (TS) modification to the parent NS conservation principles statements. Phase velocity and amplification factor error analyses are enabled via weak form discretized implementations assembled at the generic node. The parameterized error statement is then resolved into a Taylor series expansion in non-dimensional wave number space, admitting identifications that progressively annihilate lowest order error terms. The theory computational implementation is via a Galerkin weak statement on the TS modified formulation, discretely implemented using linear and bi-linear finite element basis functions for one and two dimensions respectively. The theory is extended to one dimension FE quadratic basis. A general formulation for TWS class of algorithms enabling analysis for phase accuracy is derived. Matrix stability analysis approach pertinent to TWS algorithms is presented. Theory suggested results are ported to other verification and validation problems and analyzed for solution fidelity. One dimensional space test cases include advection-diffusion and non-linear Burgers equation. Two-dimensional space test cases include a pure advection verification problem, an advection-diffusion-source verification problem and 8x1 full Navier-Stokes validation-class thermal cavity problem. Algorithm predictability is also compared for the selected algorithms on non-uniform Cartesian and regular but non-Cartesian triangular mesh. A computational approach to obtain progressively higher order phase accurate solutions using a Matlab enabled optimization theory has also been examined. The unusual behavior algorithms thus generated are analyzed under the anomalous behavior topic generated by this approach.
This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, residual distribution, finite volume, differential quadrature, spectral volume, spectral difference, PNPM, and correction procedure via reconstruction methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an understanding of the state of the art and remaining challenges in high-order CFD methods.
This informal introduction to computational fluid dynamics and practical guide to numerical simulation of transport phenomena covers the derivation of the governing equations, construction of finite element approximations, and qualitative properties of numerical solutions, among other topics. To make the book accessible to readers with diverse interests and backgrounds, the authors begin at a basic level and advance to numerical tools for increasingly difficult flow problems, emphasizing practical implementation rather than mathematical theory.?Finite Element Methods for Computational Fluid Dynamics: A Practical Guide?explains the basics of the finite element method (FEM) in the context of simple model problems, illustrated by numerical examples. It comprehensively reviews stabilization techniques for convection-dominated transport problems, introducing the reader to streamline diffusion methods, Petrov?Galerkin approximations, Taylor?Galerkin schemes, flux-corrected transport algorithms, and other nonlinear high-resolution schemes, and covers Petrov?Galerkin stabilization, classical projection schemes, Schur complement solvers, and the implementation of the k-epsilon turbulence model in its presentation of the FEM for incompressible flow problem. The book also describes the open-source finite element library ELMER, which is recommended as a software development kit for advanced applications in an online component.?
A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
The theories describing seemingly unrelated areas of physics have surprising analogies that have aroused the curiosity of scientists and motivated efforts to identify reasons for their existence. Comparative study of physical theories has revealed the presence of a common topological and geometric structure. The Mathematical Structure of Classical and Relativistic Physics is the first book to analyze this structure in depth, thereby exposing the relationship between (a) global physical variables and (b) space and time elements such as points, lines, surfaces, instants, and intervals. Combining this relationship with the inner and outer orientation of space and time allows one to construct a classification diagram for variables, equations, and other theoretical characteristics. The book is divided into three parts. The first introduces the framework for the above-mentioned classification, methodically developing a geometric and topological formulation applicable to all physical laws and properties; the second applies this formulation to a detailed study of particle dynamics, electromagnetism, deformable solids, fluid dynamics, heat conduction, and gravitation. The third part further analyses the general structure of the classification diagram for variables and equations of physical theories. Suitable for a diverse audience of physicists, engineers, and mathematicians, The Mathematical Structure of Classical and Relativistic Physics offers a valuable resource for studying the physical world. Written at a level accessible to graduate and advanced undergraduate students in mathematical physics, the book can be used as a research monograph across various areas of physics, engineering and mathematics, and as a supplemental text for a broad range of upper-level scientific coursework.