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Computational Fluid Dynamics

Author: Frederic Magoules
Publisher: CRC Press
ISBN: 1439856613
Size: 76.10 MB
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Exploring new variations of classical methods as well as recent approaches appearing in the field, Computational Fluid Dynamics demonstrates the extensive use of numerical techniques and mathematical models in fluid mechanics. It presents various numerical methods, including finite volume, finite difference, finite element, spectral, smoothed particle hydrodynamics (SPH), mixed-element-volume, and free surface flow. Taking a unified point of view, the book first introduces the basis of finite volume, weighted residual, and spectral approaches. The contributors present the SPH method, a novel approach of computational fluid dynamics based on the mesh-free technique, and then improve the method using an arbitrary Lagrange Euler (ALE) formalism. They also explain how to improve the accuracy of the mesh-free integration procedure, with special emphasis on the finite volume particle method (FVPM). After describing numerical algorithms for compressible computational fluid dynamics, the text discusses the prediction of turbulent complex flows in environmental and engineering problems. The last chapter explores the modeling and numerical simulation of free surface flows, including future behaviors of glaciers. The diverse applications discussed in this book illustrate the importance of numerical methods in fluid mechanics. With research continually evolving in the field, there is no doubt that new techniques and tools will emerge to offer greater accuracy and speed in solving and analyzing even more fluid flow problems.

Numerical Techniques For Direct And Large Eddy Simulations

Author: Xi Jiang
Publisher: CRC Press
ISBN: 9781420075793
Size: 36.18 MB
Format: PDF
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Compared to the traditional modeling of computational fluid dynamics, direct numerical simulation (DNS) and large-eddy simulation (LES) provide a very detailed solution of the flow field by offering enhanced capability in predicting the unsteady features of the flow field. In many cases, DNS can obtain results that are impossible using any other means while LES can be employed as an advanced tool for practical applications. Focusing on the numerical needs arising from the applications of DNS and LES, Numerical Techniques for Direct and Large-Eddy Simulations covers basic techniques for DNS and LES that can be applied to practical problems of flow, turbulence, and combustion. After introducing Navier–Stokes equations and the methodologies of DNS and LES, the book discusses boundary conditions for DNS and LES, along with time integration methods. It then describes the numerical techniques used in the DNS of incompressible and compressible flows. The book also presents LES techniques for simulating incompressible and compressible flows. The final chapter explores current challenges in DNS and LES. Helping readers understand the vast amount of literature in the field, this book explains how to apply relevant numerical techniques for practical computational fluid dynamics simulations and implement these methods in fluid dynamics computer programs.

Parallel Algorithms

Author: Henri Casanova
Publisher: CRC Press
ISBN: 1584889462
Size: 21.61 MB
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Focusing on algorithms for distributed-memory parallel architectures, Parallel Algorithms presents a rigorous yet accessible treatment of theoretical models of parallel computation, parallel algorithm design for homogeneous and heterogeneous platforms, complexity and performance analysis, and essential notions of scheduling. The book extracts fundamental ideas and algorithmic principles from the mass of parallel algorithm expertise and practical implementations developed over the last few decades. In the first section of the text, the authors cover two classical theoretical models of parallel computation (PRAMs and sorting networks), describe network models for topology and performance, and define several classical communication primitives. The next part deals with parallel algorithms on ring and grid logical topologies as well as the issue of load balancing on heterogeneous computing platforms. The final section presents basic results and approaches for common scheduling problems that arise when developing parallel algorithms. It also discusses advanced scheduling topics, such as divisible load scheduling and steady-state scheduling. With numerous examples and exercises in each chapter, this text encompasses both the theoretical foundations of parallel algorithms and practical parallel algorithm design.

Numerical Methods And Optimization

Author: Sergiy Butenko
Publisher: CRC Press
ISBN: 1466577789
Size: 53.33 MB
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For students in industrial and systems engineering (ISE) and operations research (OR) to understand optimization at an advanced level, they must first grasp the analysis of algorithms, computational complexity, and other concepts and modern developments in numerical methods. Satisfying this prerequisite, Numerical Methods and Optimization: An Introduction combines the materials from introductory numerical methods and introductory optimization courses into a single text. This classroom-tested approach enriches a standard numerical methods syllabus with optional chapters on numerical optimization and provides a valuable numerical methods background for students taking an introductory OR or optimization course. The first part of the text introduces the necessary mathematical background, the digital representation of numbers, and different types of errors associated with numerical methods. The second part explains how to solve typical problems using numerical methods. Focusing on optimization methods, the final part presents basic theory and algorithms for linear and nonlinear optimization. The book assumes minimal prior knowledge of the topics. Taking a rigorous yet accessible approach to the material, it includes some mathematical proofs as samples of rigorous analysis but in most cases, uses only examples to illustrate the concepts. While the authors provide a MATLAB® guide and code available for download, the book can be used with other software packages.

Computational Methods In Plasma Physics

Author: Stephen Jardin
Publisher: CRC Press
ISBN: 9781439810958
Size: 27.35 MB
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Assuming no prior knowledge of plasma physics or numerical methods, Computational Methods in Plasma Physics covers the computational mathematics and techniques needed to simulate magnetically confined plasmas in modern magnetic fusion experiments and future magnetic fusion reactors. Largely self-contained, the text presents the basic concepts necessary for the numerical solution of partial differential equations. Along with discussing numerical stability and accuracy, the author explores many of the algorithms used today in enough depth so that readers can analyze their stability, efficiency, and scaling properties. He focuses on mathematical models where the plasma is treated as a conducting fluid, since this is the most mature plasma model and most applicable to experiments. The book also emphasizes toroidal confinement geometries, particularly the tokamak—a very successful configuration for confining a high-temperature plasma. Many of the basic numerical techniques presented are also appropriate for equations encountered in a higher-dimensional phase space. One of the most challenging research areas in modern science is to develop suitable algorithms that lead to stable and accurate solutions that can span relevant time and space scales. This book provides an excellent working knowledge of the algorithms used by the plasma physics community, helping readers on their way to more advanced study.

Supercomputing

Author: Julian M. Kunkel
Publisher: Springer
ISBN: 3319075187
Size: 69.17 MB
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This book constitutes the refereed proceedings of the 29th International Supercomputing Conference, ISC 2014, held in Leipzig, Germany, in June 2014. The 34 revised full papers presented together were carefully reviewed and selected from 79 submissions. The papers cover the following topics: scalable applications with 50K+ cores; advances in algorithms; scientific libraries; programming models; architectures; performance models and analysis; automatic performance optimization; parallel I/O and energy efficiency.

Pricing Derivatives Under L Vy Models

Author: Andrey Itkin
Publisher: Birkhäuser
ISBN: 1493967924
Size: 10.54 MB
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This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solving some typical problems encountered in computational finance, including structural default models with jumps, and local stochastic volatility models with stochastic interest rates and jumps. The author also adds extra complexity to the traditional statements of these problems by taking into account jumps in each stochastic component while all jumps are fully correlated, and shows how this setting can be efficiently addressed within the framework of the new method. Written for non-mathematicians, this book will appeal to financial engineers and analysts, econophysicists, and researchers in applied numerical analysis. It can also be used as an advance course on modern finite-difference methods or computational finance.

Computational Hydrodynamics Of Capsules And Biological Cells

Author: Constantine Pozrikidis
Publisher: CRC Press
ISBN: 9781439820063
Size: 14.49 MB
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Spanning biological, mathematical, computational, and engineering sciences, computational biofluiddynamics addresses a diverse family of problems involving fluid flow inside and around living organisms, organs, tissue, biological cells, and other biological materials. Computational Hydrodynamics of Capsules and Biological Cells provides a comprehensive, rigorous, and current introduction to the fundamental concepts, mathematical formulation, alternative approaches, and predictions of this evolving field. In the first several chapters on boundary-element, boundary-integral, and immersed-boundary methods, the book covers the flow-induced deformation of idealized two-dimensional red blood cells in Stokes flow, capsules with spherical unstressed shapes based on direct and variational formulations, and cellular flow in domains with complex geometry. It also presents simulations of microscopic hemodynamics and hemorheology as well as results on the deformation of capsules and cells in dilute and dense suspensions. The book then describes a discrete membrane model where a surface network of viscoelastic links emulates the spectrin network of the cytoskeleton, before presenting a novel two-dimensional model of red and white blood cell motion. The final chapter discusses the numerical simulation of platelet motion near a wall representing injured tissue. This volume provides a roadmap to the current state of the art in computational cellular mechanics and biofluiddynamics. It also indicates areas for further work on mathematical formulation and numerical implementation and identifies physiological problems that need to be addressed in future research. MATLAB® code and other data are available at http://dehesa.freeshell.org/CC2

Decomposition Methods For Differential Equations

Author: Juergen Geiser
Publisher: CRC Press
ISBN: 9781439810972
Size: 37.38 MB
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Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and consistency analysis of the decomposition methods, and numerical results. The book focuses on the modeling of selected multi-physics problems, before introducing decomposition analysis. It presents time and space discretization, temporal decomposition, and the combination of time and spatial decomposition methods for parabolic and hyperbolic equations. The author then applies these methods to numerical problems, including test examples and real-world problems in physical and engineering applications. For the computational results, he uses various software tools, such as MATLAB®, R3T, WIAS-HiTNIHS, and OPERA-SPLITT. Exploring iterative operator-splitting methods, this book shows how to use higher-order discretization methods to solve differential equations. It discusses decomposition methods and their effectiveness, combination possibility with discretization methods, multi-scaling possibilities, and stability to initial and boundary values problems.

Verification And Validation In Scientific Computing

Author: William L. Oberkampf
Publisher: Cambridge University Press
ISBN: 1139491768
Size: 39.47 MB
Format: PDF, ePub
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Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.