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The finite element method for fluid dynamics / O. C. Zienkiewicz; R. L. Taylor; P. Nithiarasu
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: The Finite Element Method SerPublisher: Amsterdam ; Heidelberg [u.a.] : Elsevier Butterworth-Heinemann, 2014Edition: 7. ed. (Online-Ausg.)Description: Online-Ressource (1 online resource (1 online resource.))ISBN:- 9781306160902
- 1306160901
- 9780080951379
- 9781856176354
- 620.1060151825
- 620.1064
- 620.10601515353
- 624.1 624.171
- TA357
- TA640.2 .Z5 2013
Contents:
Summary: 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.Summary: Intro -- Half Title -- Author Biography -- Title Page -- Copyright -- Dedication -- Contents -- List of Figures -- List of Tables -- Preface -- 1 Introduction to the Equations of Fluid Dynamics and the Finite Element Approximation -- 1.1 General remarks and classification of fluid dynamics -- 1.2 The governing equations of fluid dynamics -- 1.2.1 Velocity, strain rates, and stresses in fluids -- 1.2.2 Constitutive relations for fluids -- 1.2.3 Mass conservation -- 1.2.4 Momentum conservation: Dynamic equilibrium -- 1.2.5 Energy conservation and equation of state -- 1.2.6 Boundary conditions -- 1.2.7 Navier-Stokes and Euler equations -- 1.3 Inviscid, incompressible flow -- 1.3.1 Velocity potential solution -- 1.4 Incompressible (or nearly incompressible) flows -- 1.5 Numerical solutions -- 1.5.1 Strong and weak forms -- 1.5.1.1 Weak form of equations -- 1.5.2 Weighted residual approximation -- 1.5.3 The Galerkin finite element method -- 1.5.4 A finite volume approximation -- 1.6 Concluding remarks -- References -- 2 Convection-Dominated Problems: Finite Element Approximations to the Convection-Diffusion-Reaction Equation -- 2.1 Introduction -- 2.2 The steady-state problem in one dimension -- 2.2.1 General remarks -- 2.2.2 Petrov-Galerkin methods for upwinding in one dimension -- 2.2.2.1 Continuity requirements for weighting functions -- 2.2.3 Balancing diffusion in one dimension -- 2.2.4 A variational principle in one dimension -- 2.2.5 Galerkin least-squares approximation (GLS) in one dimension -- 2.2.6 Subgrid scale (SGS) approximation -- 2.2.7 The finite increment calculus (FIC) for stabilizing the convective-diffusion equation in one dimension -- 2.2.8 Higher-order approximations -- 2.3 The steady-state problem in two (or three) dimensions -- 2.3.1 General remarks -- 2.3.2 Streamline (upwind) Petrov-Galerkin weighting (SUPG).PPN: PPN: 811448312Package identifier: Produktsigel: ZDB-26-MYL | ZDB-30-PAD | ZDB-30-PQE
Half Title; Author Biography; Title Page; Copyright; Dedication; Contents; List of Figures; List of Tables; Preface; 1 Introduction to the Equations of Fluid Dynamics and the Finite Element Approximation; 1.1 General remarks and classification of fluid dynamics; 1.2 The governing equations of fluid dynamics; 1.2.1 Velocity, strain rates, and stresses in fluids; 1.2.2 Constitutive relations for fluids; 1.2.3 Mass conservation; 1.2.4 Momentum conservation: Dynamic equilibrium; 1.2.5 Energy conservation and equation of state; 1.2.6 Boundary conditions; 1.2.7 Navier-Stokes and Euler equations
1.3 Inviscid, incompressible flow1.3.1 Velocity potential solution; 1.4 Incompressible (or nearly incompressible) flows; 1.5 Numerical solutions; 1.5.1 Strong and weak forms; 1.5.1.1 Weak form of equations; 1.5.2 Weighted residual approximation; 1.5.3 The Galerkin finite element method; 1.5.4 A finite volume approximation; 1.6 Concluding remarks; References; 2 Convection-Dominated Problems: Finite Element Approximations to the Convection-Diffusion-Reaction Equation; 2.1 Introduction; 2.2 The steady-state problem in one dimension; 2.2.1 General remarks
2.2.2 Petrov-Galerkin methods for upwinding in one dimension2.2.2.1 Continuity requirements for weighting functions; 2.2.3 Balancing diffusion in one dimension; 2.2.4 A variational principle in one dimension; 2.2.5 Galerkin least-squares approximation (GLS) in one dimension; 2.2.6 Subgrid scale (SGS) approximation; 2.2.7 The finite increment calculus (FIC) for stabilizing the convective-diffusion equation in one dimension; 2.2.8 Higher-order approximations; 2.3 The steady-state problem in two (or three) dimensions; 2.3.1 General remarks
2.3.2 Streamline (upwind) Petrov-Galerkin weighting (SUPG)2.3.3 Galerkin least squares (GLS) and finite increment calculus (FIC) in multidimensional problems; 2.4 Steady state: Concluding remarks; 2.5 Transients: Introductory remarks; 2.5.1 Mathematical background; 2.5.2 Possible discretization procedures; 2.6 Characteristic-based methods; 2.6.1 Mesh updating and interpolation methods; 2.6.2 Characteristic-Galerkin procedures; 2.6.3 A simple explicit characteristic-Galerkin procedure; 2.6.4 Boundary conditions: Radiation; 2.7 Taylor-Galerkin procedures for scalar variables
2.8 Steady-state condition2.9 Nonlinear waves and shocks; 2.10 Treatment of pure convection; 2.11 Boundary conditions for convection-diffusion; 2.12 Summary and concluding remarks; References; 3 The Characteristic-Based Split (CBS) Algorithm: A General Procedure for Compressible and Incompressible Flow; 3.1 Introduction; 3.2 Nondimensional form of the governing equations; 3.3 Characteristic-based split (CBS) algorithm; 3.3.1 The split: General remarks; 3.3.2 The split: Temporal discretization; 3.3.3 Spatial discretization and solution procedure; 3.3.4 Mass diagonalization (lumping)
3.4 Explicit, semi-implicit, and nearly implicit forms
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