Simulation of Manufacturing Sequences of Functionally Graded Structures
Simulation of Manufacturing Sequences of Functionally Graded Structures

Author: Gleim, Tobias

Publisher: kassel university press GmbH

Published: 2017-02-10

Total Pages: 339

ISBN-13: 3737602506

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The current paper establishes an axisymmetric model for an inductive heating process. Therein, the fully coupled MAXWELL equations, assuming a temperature dependent permeability, are combined with the non-linear heat conduction equation to yield a monolithic solution strategy. The latter is based on a consistent linearization together with a higher order finite element discretization using GALERKIN'S method in space. For the temporal discretization, the generalized Newmark-? methods, higher order RUNGE-KUTTA methods, and discontinuous and continuous GALERKIN methods are used. Furthermore, the residual error is introduced to open an alternative way to obtain a numerically efficient estimation of the time integration accuracy. Simulation results of the electric, magnetic and thermal fields are provided, together with parameter studies concerning spatial discretization, frequency dependence and penetration depth of the heating zone. Another topic analyzed is the residual error and its estimation quality regarding polynomial degree and time step size. A further aspect of this work is the investigation of the thermal fluid-structure interaction with respect to functionally graded materials. Different coupling strategies for the acceleration of the fixed-point iteration in each time step is in the foreground. Relaxation methods as well as extrapolation methods make it possible to significantly reduce the number of fixed point iterations. At the same time, an adaptive strategy with higher order RUNGE-KUTTA methods can provide a further advantage in combination with acceleration methods.

Computational Fluid Dynamics
Computational Fluid Dynamics

Author: Jiyuan Tu

Publisher: Elsevier

Published: 2023-05-09

Total Pages: 498

ISBN-13: 0323939392

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Computational Fluid Dynamics: A Practical Approach, Fourth Edition is an introduction to computational fluid dynamics (CFD) fundamentals and commercial CFD software to solve engineering problems. The book is designed for a wide variety of engineering students new to CFD, but is also ideal for practicing engineers learning CFD for the first time. Combining an appropriate level of mathematical background, worked examples, computer screen shots, and step-by-step processes, this book walks the reader through modeling and computing, as well as interpreting CFD results. This new edition has been updated throughout, with new content and improved figures, examples and problems. Updated throughout, with new case studies, examples, references, and corrections according to readers’ and reviewers’ feedback Delivers the latest developments in CFD including the high-order and reduced-order modeling approach, machine learning–accelerated CFD, full coverage of high-speed fluid dynamics, and the meshless approaches to provide a broader overview of the application areas where CFD can be used Reorganized and rewritten to better meet the needs of CFD instructors and students Online resources include all lecturing and guest lecturing PPTs, computer lab practicing with step-by-step and screenshot guidelines, assignment and course project details, answers for review questions in each chapter, a new bonus chapter featuring detailed case studies, and result discussion

Mesh Methods
Mesh Methods

Author: Viktor A. Rukavishnikov

Publisher: MDPI

Published: 2021-03-29

Total Pages: 128

ISBN-13: 3036503765

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Mathematical models of various natural processes are described by differential equations, systems of partial differential equations and integral equations. In most cases, the exact solution to such problems cannot be determined; therefore, one has to use grid methods to calculate an approximate solution using high-performance computing systems. These methods include the finite element method, the finite difference method, the finite volume method and combined methods. In this Special Issue, we bring to your attention works on theoretical studies of grid methods for approximation, stability and convergence, as well as the results of numerical experiments confirming the effectiveness of the developed methods. Of particular interest are new methods for solving boundary value problems with singularities, the complex geometry of the domain boundary and nonlinear equations. A part of the articles is devoted to the analysis of numerical methods developed for calculating mathematical models in various fields of applied science and engineering applications. As a rule, the ideas of symmetry are present in the design schemes and make the process harmonious and efficient.

First International Congress of Chinese Mathematicians
First International Congress of Chinese Mathematicians

Author: Stephen Shing-Toung Yau

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 596

ISBN-13: 0821826522

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The International Congress of Mathematicians was an historical event that was held at the Morningside Center of Mathematics of the Chinese Academy of Sciences (Beijing). It was the first occasion where Chinese mathematicians from all over the world gathered to present their research. The Morningside Mathematics lectures were given by R. Borcherds, J. Coates, R. Graham, and D. Stroock. Other distinguished speakers included J.-P. Bourguignon, J. Jöst, M. Taylor, and S. L. Lee. Topics covered in the volume include algebra and representation theory, algebraic geometry, number theory and automorphic forms, Riemannian geometry and geometric analysis, mathematical physics, topology, complex analysis and complex geometry, computational mathematics, and combinatorics. Titles in this series are copublished with International Press, Cambridge, MA.

Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids
Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids

Author: Laura De Lorenzis

Publisher: Springer Nature

Published: 2020-02-08

Total Pages: 225

ISBN-13: 3030375188

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The book examines innovative numerical methods for computational solid and fluid mechanics that can be used to model complex problems in engineering. It also presents innovative and promising simulation methods, including the fundamentals of these methods, as well as advanced topics and complex applications. Further, the book explores how numerical simulations can significantly reduce the number of time-consuming and expensive experiments required, and can support engineering decisions by providing data that would be very difficult, if not impossible, to obtain experimentally. It also includes chapters covering topics such as particle methods addressing particle-based materials and numerical methods that are based on discrete element formulations; fictitious domain methods; phase field models; computational fluid dynamics based on modern finite volume schemes; hybridizable discontinuous Galerkin methods; and non-intrusive coupling methods for structural models.

Geoid Determination
Geoid Determination

Author: Fernando Sansò

Publisher: Springer Science & Business Media

Published: 2013-02-13

Total Pages: 748

ISBN-13: 3540747001

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This book will be based on the material of the lecture noties in several International Schools for the Determination and Use of the Geoid, organized by the International Geoid Serivice of the International Association of Geodesy. It consolidates, unifies, and streamlines this material in a unique way not covereed by the few other books that exist on this subjext. More specifically, the book presents (for the first time in a single volume) the theory and methodology of the most common technique used for precise determination of the geoid, including the computation of the marine geoid from satellite altimetry data. These are illustrated by specific examples and actual computations of local geoids. In addition, the book provides the fundamentals of estimating orthometric heights without spirit levelling, by properly combining a geoid with heights from GPS. Besides the geodectic and geophysical uses, this last application has made geoid computation methods very popular in recent years because the entire GPS and GIS user communities are interested in estimating geoid undulations in order to convert GPS heights to physically meaningful orthometric heights (elevations above mean sea level). The overall purpose of the book is, therefore, to provide the user community (academics, graduate students, geophysicists, engineers, oceanographers, GIS and GPS users, researchers) with a self-contained textbook, which will supply them with the complete roadmap of estimating geoid undulations, from the theoretical definitions and formulas to the available numerical methods and their implementation and the test in practice.

Interface Problems And Methods In Biological And Physical Flows
Interface Problems And Methods In Biological And Physical Flows

Author: Boo Cheong Khoo

Publisher: World Scientific

Published: 2009-05-05

Total Pages: 184

ISBN-13: 9814468983

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This volume showcases lecture notes collected from tutorials presented at the Workshop on Moving Interface Problems and Applications in Fluid Dynamics that was held between January 8 and March 31, 2007 at the Institute for Mathematical Sciences, National University of Singapore. As part of the program, these tutorials were conducted by specialists within their respective areas such as Robert Dillon, Zhilin Li, John Lowengrub, Frank Lu and Gretar Tryggvason.The topics in the program encompass modeling and simulations of biological flow coupled to deformable tissue/elastic structure, shock wave and bubble dynamics and various applications like biological treatments with experimental verification, multi-medium flow or multiphase flow and various applications including cavitation/supercavitation, detonation problems, Newtonian and non-Newtonian fluid, and many other areas.This volume benefits graduate students and researchers keen in the field of interfacial flows for application to physical and biological systems. Even beginners will find this volume a very useful starting point with many relevant references applicable.