Development of Reduced-order Meshless Solutions of Three-dimensional Navier Sokes Transport Phenomena

Development of Reduced-order Meshless Solutions of Three-dimensional Navier Sokes Transport Phenomena

Author: Daniel Benjamin Work

Publisher:

Published: 2006

Total Pages:

ISBN-13:

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Abstract: Emerging meshless technologies are very promising for numerically solving Euler and Navier-Stokes transport systems in one-, two-, and three-dimensions (3-D). The Reduced-Order Meshless (ROM) technique developed in this work is applicable to a wide array of transport physics systems (i.e., fluid flow, heat transfer, gas dynamics, internal combustion flow and chemical reactions, and solid-liquid mixture flow) with various types of boundary and initial conditions. Such applications to be benchmarked in this work include one- and two-dimensional advection, and two- and three-dimensional convection-diffusion problems (Burgers' equation). Computational solutions to these boundary-value problems will be demonstrated using the ROM approach and the predicted solutions will be posted against the Meshless Local Petrov-Galerkin (MLPG) method and exact solutions to these problems when they exist. Extensions to 3-D phenomenology will be attempted based on the conclusions obtained from computational studies to establish the existence, smoothness, and boundedness of 3-D Navier-Stokes transport systems. An approximated benchmark solution of the Navier-Stokes equations is also developed in this work using a linearized perturbation analysis. The classical paper on gas turbine throughflow, Three Dimensional Flows in Turbomachines (Marble, 1964), outlines this procedure for approximation, and produces solutions for a class of axisymmetric problems. An investigation into the behavior of these solutions uncovered a series of inconsistencies in the paper, which are outlined in detail and corrected when known to be in error.


Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations

Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations

Author: Ivo Babuska

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 487

ISBN-13: 1461242487

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With considerations such as complex-dimensional geometries and nonlinearity, the computational solution of partial differential systems has become so involved that it is important to automate decisions that have been normally left to the individual. This book covers such decisions: 1) mesh generation with links to the software generating the domain geometry, 2) solution accuracy and reliability with mesh selection linked to solution generation. This book is suited for mathematicians, computer scientists and engineers and is intended to encourage interdisciplinary interaction between the diverse groups.


Very Large Floating Structures

Very Large Floating Structures

Author: C.M. Wang

Publisher: CRC Press

Published: 2007-09-12

Total Pages: 251

ISBN-13: 0203934601

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Groundbreaking and comprizing articles by expert contributors, this volume provides a comprehensive treatment of VLFSs and their relationship with the sea, marine habitats, the pollution of costal waters and tidal and natural current flow. It looks in-depth at: VLFS and the colonization of ocean space with their appearance in the waters off developed coastal cities wave properties, which is essential for estimating the loading on the VLFS as well as for modelling structure-fluid interactions hydroelastic and structural analysis of VLFS at an overall level and the cell level the analysis and design of breakwaters simulation models to understand the actual flow of water through the VLFS and to determine the drift forces for the mooring systems anti-corrosion and maintenance systems new research and developments, with emphasis on the Mega-Float, a 1 km long floating test runway. Well-illustrated with photographs, drawings, equations for mathematical modelling and analysis and extensively referenced, Very Large Floating Structures is ideal for professionals, academics and students of civil and structural engineering.


The Finite Volume Method in Computational Fluid Dynamics

The Finite Volume Method in Computational Fluid Dynamics

Author: F. Moukalled

Publisher: Springer

Published: 2015-08-13

Total Pages: 799

ISBN-13: 3319168746

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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.


Computational Hydraulics

Computational Hydraulics

Author: Ioana Popescu

Publisher: IWA Publishing

Published: 2014-08-14

Total Pages: 184

ISBN-13: 1780400446

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Computational Hydraulics introduces the concept of modeling and the contribution of numerical methods and numerical analysis to modeling. It provides a concise and comprehensive description of the basic hydraulic principles, and the problems addressed by these principles in the aquatic environment. Flow equations, numerical and analytical solutions are included. The necessary steps for building and applying numerical methods in hydraulics comprise the core of the book and this is followed by a report of different example applications of computational hydraulics: river training effects on flood propagation, water quality modelling of lakes and coastal applications. The theory and exercises included in the book promote learning of concepts within academic environments. Sample codes are made available online for purchasers of the book. Computational Hydraulics is intended for under-graduate and graduate students, researchers, members of governmental and non-governmental agencies and professionals involved in management of the water related problems. Author: Ioana Popescu, Hydroinformatics group, UNESCO-IHE Institute for Water Education, Delft , The Netherlands.


Fundamentals of the Finite Element Method for Heat and Fluid Flow

Fundamentals of the Finite Element Method for Heat and Fluid Flow

Author: Roland W. Lewis

Publisher: John Wiley and Sons

Published: 2008-02-07

Total Pages: 357

ISBN-13: 0470346388

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Heat transfer is the area of engineering science which describes the energy transport between material bodies due to a difference in temperature. The three different modes of heat transport are conduction, convection and radiation. In most problems, these three modes exist simultaneously. However, the significance of these modes depends on the problems studied and often, insignificant modes are neglected. Very often books published on Computational Fluid Dynamics using the Finite Element Method give very little or no significance to thermal or heat transfer problems. From the research point of view, it is important to explain the handling of various types of heat transfer problems with different types of complex boundary conditions. Problems with slow fluid motion and heat transfer can be difficult problems to handle. Therefore, the complexity of combined fluid flow and heat transfer problems should not be underestimated and should be dealt with carefully. This book: Is ideal for teaching senior undergraduates the fundamentals of how to use the Finite Element Method to solve heat transfer and fluid dynamics problems Explains how to solve various heat transfer problems with different types of boundary conditions Uses recent computational methods and codes to handle complex fluid motion and heat transfer problems Includes a large number of examples and exercises on heat transfer problems In an era of parallel computing, computational efficiency and easy to handle codes play a major part. Bearing all these points in mind, the topics covered on combined flow and heat transfer in this book will be an asset for practising engineers and postgraduate students. Other topics of interest for the heat transfer community, such as heat exchangers and radiation heat transfer, are also included.


The Finite Element Method: Theory, Implementation, and Applications

The Finite Element Method: Theory, Implementation, and Applications

Author: Mats G. Larson

Publisher: Springer Science & Business Media

Published: 2013-01-13

Total Pages: 403

ISBN-13: 3642332870

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This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​


An Introduction to Fluid Mechanics and Transport Phenomena

An Introduction to Fluid Mechanics and Transport Phenomena

Author: G. Hauke

Publisher: Springer Science & Business Media

Published: 2008-08-26

Total Pages: 301

ISBN-13: 1402085370

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This book presents the foundations of fluid mechanics and transport phenomena in a concise way. It is suitable as an introduction to the subject as it contains many examples, proposed problems and a chapter for self-evaluation.


Symmetry and Fluid Mechanics

Symmetry and Fluid Mechanics

Author: Rahmat Ellahi

Publisher: MDPI

Published: 2020-03-25

Total Pages: 446

ISBN-13: 3039284266

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Since the 1980s, attention has increased in the research of fluid mechanics due to its wide application in industry and phycology. Major advances have occurred in the modeling of key topics such Newtonian and non-Newtonian fluids, nanoparticles, thermal management, and physiological fluid phenomena in biological systems, which have been published in this Special Issue on symmetry and fluid mechanics for Symmetry. Although, this book is not a formal textbook, it will be useful for university teachers, research students, and industrial researchers and for overcoming the difficulties that occur when considering the nonlinear governing equations. For such types of equations, obtaining an analytic or even a numerical solution is often more difficult. This book addresses this challenging job by outlining the latest techniques. In addition, the findings of the simulation are logically realistic and meet the standard of sufficient scientific value.