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Spectral/hp Element Methods for CFD

Spectral/hp Element Methods for CFD PDF Author: George Karniadakis
Publisher: Oxford University Press on Demand
ISBN: 0195102266
Category : Mathematics
Languages : en
Pages : 406
Book Description
Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrates how these methods can be applied to advection-diffusion and to incompressible and compressible Navier-Stokes equations. Drawing on both published and unpublished material, the book is an important resource for experienced researchers and for those new to the field.

Spectral/hp Element Methods for CFD

Spectral/hp Element Methods for CFD PDF Author: George Karniadakis
Publisher: Oxford University Press on Demand
ISBN: 0195102266
Category : Mathematics
Languages : en
Pages : 406
Book Description
Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrates how these methods can be applied to advection-diffusion and to incompressible and compressible Navier-Stokes equations. Drawing on both published and unpublished material, the book is an important resource for experienced researchers and for those new to the field.

Spectral/hp Element Methods for Computational Fluid Dynamics

Spectral/hp Element Methods for Computational Fluid Dynamics PDF Author: George Karniadakis
Publisher: Oxford University Press
ISBN: 0199671362
Category : Mathematics
Languages : en
Pages : 676
Book Description
Revision of: Spectral/hp element methods for CFD. 1999.

Introduction to Finite and Spectral Element Methods Using MATLAB

Introduction to Finite and Spectral Element Methods Using MATLAB PDF Author: Constantine Pozrikidis
Publisher: CRC Press
ISBN: 1482209160
Category : Mathematics
Languages : en
Pages : 832
Book Description
Incorporating new topics and original material, Introduction to Finite and Spectral Element Methods Using MATLAB, Second Edition enables readers to quickly understand the theoretical foundation and practical implementation of the finite element method and its companion spectral element method. Readers gain hands-on computational experience by using

Advanced Finite Element Methods and Applications

Advanced Finite Element Methods and Applications PDF Author: Thomas Apel
Publisher: Springer Science & Business Media
ISBN: 3642303161
Category : Technology & Engineering
Languages : en
Pages : 376
Book Description
This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods. Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.

The Finite Element Method for Fluid Dynamics

The Finite Element Method for Fluid Dynamics PDF Author: Olek C Zienkiewicz
Publisher: Butterworth-Heinemann
ISBN: 0080951376
Category : Technology & Engineering
Languages : en
Pages : 584
Book Description
The Finite Element Method for Fluid Dynamics offers a complete introduction the application of the finite element method to fluid mechanics. The book begins with a useful summary of all relevant partial differential equations before moving on to discuss convection stabilization procedures, steady and transient state equations, and numerical solution of fluid dynamic equations. The character-based split (CBS) scheme is introduced and discussed in detail, followed by thorough coverage of incompressible and compressible fluid dynamics, flow through porous media, shallow water flow, and the numerical treatment of long and short waves. Updated throughout, this new edition includes new chapters on: Fluid-structure interaction, including discussion of one-dimensional and multidimensional problems Biofluid dynamics, covering flow throughout the human arterial system Focusing on the core knowledge, mathematical and analytical tools needed for successful computational fluid dynamics (CFD), The Finite Element Method for Fluid Dynamics is the authoritative introduction of choice for graduate level students, researchers and professional engineers. A proven keystone reference in the library of any engineer needing to understand and apply the finite element method to fluid mechanics Founded by an influential pioneer in the field and updated in this seventh edition by leading academics who worked closely with Olgierd C. Zienkiewicz Features new chapters on fluid-structure interaction and biofluid dynamics, including coverage of one-dimensional flow in flexible pipes and challenges in modeling systemic arterial circulation

hp-Finite Element Methods for Singular Perturbations

hp-Finite Element Methods for Singular Perturbations PDF Author: Jens M. Melenk
Publisher: Springer
ISBN: 354045781X
Category : Mathematics
Languages : en
Pages : 326
Book Description
Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.

Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012

Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 PDF Author: Mejdi Azaïez
Publisher: Springer Science & Business Media
ISBN: 3319016016
Category : Mathematics
Languages : en
Pages : 425
Book Description
The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2012), and provides an overview of the depth and breath of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography. ​

Advanced Computational Methods in Science and Engineering

Advanced Computational Methods in Science and Engineering PDF Author: Barry Koren
Publisher: Springer Science & Business Media
ISBN: 3642033873
Category : Mathematics
Languages : en
Pages : 501
Book Description
The aim of the present book is to show, in a broad and yet deep way, the state of the art in computational science and engineering. Examples of topics addressed are: fast and accurate numerical algorithms, model-order reduction, grid computing, immersed-boundary methods, and specific computational methods for simulating a wide variety of challenging problems, problems such as: fluid-structure interaction, turbulent flames, bone-fracture healing, micro-electro-mechanical systems, failure of composite materials, storm surges, particulate flows, and so on. The main benefit offered to readers of the book is a well-balanced, up-to-date overview over the field of computational science and engineering, through in-depth articles by specialists from the separate disciplines.

Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations

Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations PDF Author: Gary Cohen
Publisher: Springer
ISBN: 9401777616
Category : Technology & Engineering
Languages : en
Pages : 381
Book Description
This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulationof waves.

Domain Decomposition Methods in Science and Engineering XVI

Domain Decomposition Methods in Science and Engineering XVI PDF Author: Olof B. Widlund
Publisher: Springer Science & Business Media
ISBN: 3540344683
Category : Computers
Languages : en
Pages : 783
Book Description
Domain decomposition is an active research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models of natural and engineered systems. The present volume sets forth new contributions in areas of numerical analysis, computer science, scientific and industrial applications, and software development.