The Finite Element Method for Fluid Dynamics provides a comprehensive introduction to the application of the finite element method in fluid dynamics. The book begins with a useful summary of all relevant partial differential equations, progressing to the discussion of convection stabilization procedures, steady and transient state equations, and numerical solution of fluid dynamic equations.
In this expanded eighth edition, the book starts by explaining the character-based split (CBS) scheme, followed by an exploration of various other methods, including SUPG/PSPG, space-time, and VMS methods. Emphasising the fundamental knowledge, mathematical, and analytical tools necessary for successful implementation of computational fluid dynamics (CFD), The Finite Element Method for Fluid Dynamics stands as the authoritative introduction of choice for graduate level students, researchers, and professional engineers.
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Table of Contents
1. The equations of fluid dynamics
2. The finite element approximation
3. Convection dominated problems
finite element approximations to the convection-diffusion-reaction equation
4. Fractional step methods: the characteristic-based split (CBS) algorithm for compressible and incompressible flows
5. Incompressible Newtonian laminar flows
6. Incompressible non-Newtonian flows
7. Free surface flows
8. Buoyancy driven flows
9. Compressible high-speed gas flow
10. Adaptive mesh refinement
11. Turbulent flows
12. Flow and heat transport in porous media
13. Shallow-water problems
14. Long and medium waves
15. Short waves
16. Fluid-structure interaction
17. Biofluid dynamics
blood flow
18. Data-driven methods
19. Computer implementation of the CBS algorithm
Appendix A: Self-adjoint differential equations
Appendix B: Non-conservative form of Navier-Stokes equations
Appendix C: Computing drag force and stream function
Appendix D: Convection-diffusion equations: vector-valued variables
Appendix E: Integration formulae
Appendix F: Edge-based finite element formulation
Appendix G: Boundary layer-inviscid flow coupling
Appendix H: Multigrid method
Appendix I: Mass-weighted averaged turbulence transport equations
Appendix J: Introduction to neural networks
Authors
R. L. Taylor Emeritus Professor of Engineering, University of California, Berkeley, USA. Professor R.L. Taylor has more than 60 years of experience in the modelling and simulation of structures and solid continua including eighteen years in industry. He is Professor of the Graduate School and the Emeritus T.Y. and Margaret Lin Professor of Engineering at the University of California, Berkeley and also Corporate Fellow at Dassault Syst�mes Americas Corp. in Johnston, Rhode Island. In 1991 he was elected to membership in the US National Academy of Engineering in recognition of his educational and research contributions to the field of computational mechanics. Professor Taylor is a Fellow of the US Association for Computational Mechanics - USACM (1996) and a Fellow of the International Association of Computational Mechanics - IACM (1998). He has received numerous awards including the Berkeley Citation, the highest honour awarded by the University of California, Berkeley, the USACM John von Neumann Medal, the IACM Gauss-Newton Congress Medal and a Dr.-Ingenieur ehrenhalber awarded by the Technical University of Hannover, Germany. Professor Taylor has written several computer programs for finite element analysis of structural and non-structural systems, one of which, FEAP, is used world-wide in education and research environments. A personal version, FEAPpv, available on GitHub, is incorporated into this book. P. Nithiarasu Professor, Zienkiewicz Institute for Modelling, Data and AI and Associate Dean for Research, Innovation and Impact, Faculty of Science and Engineering, Swansea University.P. Nithiarasu is Professor at Zienkiewicz Institute for Modelling, Data and AI and Associate Dean for Research, Innovation and Impact, Faculty of Science and Engineering, Swansea University. Previously he has served as the Head of Zienkiewicz Centre for Computational Engineering, Deputy Head of College of Engineering and Dean of Academic Leadership. He was awarded the Zienkiewicz silver medal from the ICE London in 2002, the ECCOMAS Young Investigator award in 2004, and the prestigious EPSRC Advanced Fellowship in 2006.
