Advanced Reduced Order Methods And Applications In Computational Fluid Dynamics
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Advanced Reduced Order Methods And Applications In Computational Fluid Dynamics
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Author : Gianluigi Rozza
language : en
Publisher: SIAM
Release Date : 2022-11-21
Advanced Reduced Order Methods And Applications In Computational Fluid Dynamics written by Gianluigi Rozza and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-21 with Mathematics categories.
Reduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications. This book will be of interest to researchers and graduate students in the field of reduced order modeling.
The Finite Volume Method In Computational Fluid Dynamics
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Author : F. Moukalled
language : en
Publisher: Springer
Release Date : 2015-08-13
The Finite Volume Method In Computational Fluid Dynamics written by F. Moukalled and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-13 with Technology & Engineering categories.
This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.
Modeling Nonlinear Dynamics From Equations And Data With Applications To Solids Fluids And Controls
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Author : George Haller
language : en
Publisher: SIAM
Release Date : 2025-05-20
Modeling Nonlinear Dynamics From Equations And Data With Applications To Solids Fluids And Controls written by George Haller and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-20 with Computers categories.
This concise text presents an introduction to the emerging area of reducing complex nonlinear differential equations or time-resolved data sets to spectral submanifolds (SSMs). SSMs are ubiquitous low-dimensional attracting invariant manifolds that can be constructed systematically, building on the spectral properties of the linear part of a nonlinear system. The internal dynamics within SSMs then serve as exact, low-dimensional models with which the full system evolution synchronizes exponentially fast. SSM-based model reduction has a solid mathematical foundation and hence is guaranteed to deliver accurate and predictive reduced-order models under a precise set of assumptions. This book introduces the foundations of SSM theory to the novice reader; reviews recent extensions of classic SSM results for the advanced reader; and illustrates the power of SSM reduction on a large collection of equation- and data-driven applications in fluid mechanics, solid mechanics, and control. This book is intended for graduate students, postdocs, faculty, and industrial researchers working in model reduction for nonlinear physical systems arising in solid mechanics, fluid dynamics, and control theory. It is appropriate for courses on differential equations, modeling, dynamical systems, and data-driven modeling.
Spectral And High Order Methods For Partial Differential Equations Icosahom 2018
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Author : Spencer J. Sherwin
language : en
Publisher: Springer Nature
Release Date : 2020-08-11
Spectral And High Order Methods For Partial Differential Equations Icosahom 2018 written by Spencer J. Sherwin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-11 with Mathematics categories.
This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
Spectral And High Order Methods For Partial Differential Equations Icosahom 2020 1
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Author : Jens M. Melenk
language : en
Publisher: Springer Nature
Release Date : 2023-06-30
Spectral And High Order Methods For Partial Differential Equations Icosahom 2020 1 written by Jens M. Melenk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-30 with Mathematics categories.
The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed articles cover state of the art topics in high order discretizations of partial differential equations. The volume presents a wide range of topics including the design and analysis of high order methods, the development of fast solvers on modern computer architecture, and the application of these methods in fluid and structural mechanics computations.
Uncertainty Quantification
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Author : Ralph C. Smith
language : en
Publisher: SIAM
Release Date : 2024-09-13
Uncertainty Quantification written by Ralph C. Smith and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-13 with Mathematics categories.
Uncertainty quantification serves a fundamental role when establishing the predictive capabilities of simulation models. This book provides a comprehensive and unified treatment of the mathematical, statistical, and computational theory and methods employed to quantify uncertainties associated with models from a wide range of applications. Expanded and reorganized, the second edition includes advances in the field and provides a comprehensive sensitivity analysis and uncertainty quantification framework for models from science and engineering. It contains new chapters on random field representations, observation models, parameter identifiability and influence, active subspace analysis, and statistical surrogate models, and a completely revised chapter on local sensitivity analysis. Other updates to the second edition are the inclusion of over 100 exercises and many new examples — several of which include data — and UQ Crimes listed throughout the text to identify common misconceptions and guide readers entering the field. Uncertainty Quantification: Theory, Implementation, and Applications, Second Edition is intended for advanced undergraduate and graduate students as well as researchers in mathematics, statistics, engineering, physical and biological sciences, operations research, and computer science. Readers are assumed to have a basic knowledge of probability, linear algebra, differential equations, and introductory numerical analysis. The book can be used as a primary text for a one-semester course on sensitivity analysis and uncertainty quantification or as a supplementary text for courses on surrogate and reduced-order model construction and parameter identifiability analysis.
Mathematical Theory Of Finite Elements
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Author : Leszek F. Demkowicz
language : en
Publisher: SIAM
Release Date : 2023-09-22
Mathematical Theory Of Finite Elements written by Leszek F. Demkowicz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-22 with Mathematics categories.
This book discusses the foundations of the mathematical theory of finite element methods. The focus is on two subjects: the concept of discrete stability, and the theory of conforming elements forming the exact sequence. Both coercive and noncoercive problems are discussed.. Following the historical path of development, the author covers the Ritz and Galerkin methods to Mikhlin’s theory, followed by the Lax–Milgram theorem and Cea’s lemma to the Babuska theorem and Brezzi’s theory. He finishes with an introduction to the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. Based on the author’s personal lecture notes for a popular version of his graduate course on mathematical theory of finite elements, the book includes a unique exposition of the concept of discrete stability and the means to guarantee it, a coherent presentation of finite elements forming the exact grad-curl-div sequence, and an introduction to the DPG method. Intended for graduate students in computational science, engineering, and mathematics programs, Mathematical Theory of Finite Elements is also appropriate for graduate mathematics and mathematically oriented engineering students. Instructors will find the book useful for courses in real analysis, functional analysis, energy (Sobolev) spaces, and Hilbert space methods for PDEs.
Nonlocal Integral Equation Continuum Models
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Author : Marta D'Elia
language : en
Publisher: SIAM
Release Date : 2024-09-12
Nonlocal Integral Equation Continuum Models written by Marta D'Elia and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-12 with Mathematics categories.
The book presents the state of the art of nonlocal modeling and discretization and provides a practical introduction to nonlocal modeling for readers who are not familiar with such models. These models have recently become a viable alternative to classical partial differential equations when the latter are unable to capture effects such as discontinuities and multiscale behavior in a system of interest. Because of their integral nature, nonlocal operators allow for the relaxation of regularity requirements on the solution and thus allow for the capture of multiscale effects, the result of which is their successful use in many scientific and engineering applications. The book also provides a thorough analysis and numerical treatment of nonstandard nonlocal models, focusing on both well-known and nonstandard interaction neighborhoods. In addition, the book delivers an extensive practical treatment of the implementation of discretization strategies via finite element methods. Numerous figures are provided as concrete examples to illustrate both the analytic and computational results. Nonlocal Integral Equation Continuum Models: Nonstandard Interaction Neighborhoods and Finite Element Discretizations is intended for mathematical and application researchers interested in alternatives to using partial differential equation models that better describe the phenomena they are interested in. The book will also be of use to computational scientists and engineers who need to make sense of how to use available software, improve existing software, or develop new software tailored to their application interests.
Numerical Partial Differential Equations
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Author : James H. Adler
language : en
Publisher: SIAM
Release Date : 2025-03-26
Numerical Partial Differential Equations written by James H. Adler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-26 with Mathematics categories.
This comprehensive textbook focuses on numerical methods for approximating solutions to partial differential equations (PDEs). The authors present a broad survey of these methods, introducing readers to the central concepts of various families of discretizations and solution algorithms and laying the foundation needed to understand more advanced material. The authors include over 100 well-established definitions, theorems, corollaries, and lemmas and summaries of and references to in-depth treatments of more advanced mathematics when needed. Numerical Partial Differential Equations is divided into four parts: Part I covers basic background on PDEs and numerical methods. Part II introduces the three main classes of numerical methods for PDEs that are the book’s focus (finite-difference, finite-element, and finite-volume methods). Part III discusses linear solvers and finite-element and finite-volume methods at a more advanced level. Part IV presents further high-level topics on discretizations and solvers. This book is intended for advanced undergraduate/first-year graduate and advanced graduate students in applied math, as well as students in science and engineering disciplines. The book will also appeal to researchers in the field of scientific computing. Chapters are designed to be stand-alone, allowing distinct paths through the text, making it appropriate for both single-semester and multi-semester courses. It is appropriate for courses covering topics ranging from numerical methods for PDEs to numerical linear algebra.
A First Course In Linear Optimization
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Author : Amir Beck
language : en
Publisher: SIAM
Release Date : 2025-05-05
A First Course In Linear Optimization written by Amir Beck and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-05 with Mathematics categories.
This self-contained textbook provides the foundations of linear optimization, covering topics in both continuous and discrete linear optimization. It gradually builds the connection between theory, algorithms, and applications so that readers gain a theoretical and algorithmic foundation, familiarity with a variety of applications, and the ability to apply the theory and algorithms to actual problems. To deepen the reader’s understanding, the authors provide many applications from diverse areas of applied sciences, such as resource allocation, line fitting, graph coloring, the traveling salesman problem, game theory, and network flows; more than 180 exercises, most of them with partial answers and about 70 with complete solutions; and a continuous illustration of the theory through examples and exercises. A First Course in Linear Optimization is intended to be read cover to cover and requires only a first course in linear algebra as a prerequisite. Its 13 chapters can be used as lecture notes for a first course in linear optimization. This book is for a first undergraduate course in linear optimization, such as linear programming, linear optimization, and operations research. It is appropriate for students in operations research, mathematics, economics, and industrial engineering, as well as those studying computer science and engineering disciplines.