The Finite Element Method for Fluid Dynamics

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 Systèmes 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 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.

• 1. The equations of fluid dynamics2. The finite element approximation3. Convection dominated problems – finite element approximations to the convection–diffusion–reaction equation4. Fractional step methods: the characteristic-based split (CBS) algorithm for compressible and incompressible flows5. Incompressible Newtonian laminar flows6. Incompressible non-Newtonian flows7. Free surface flows8. Buoyancy driven flows9. Compressible high-speed gas flow10. Adaptive mesh refinement11. Turbulent flows12. Flow and heat transport in porous media13. Shallow-water problems14. Long and medium waves15. Short waves16. Fluid–structure interaction17. Biofluid dynamics – blood flow18. Data-driven methods19. Computer implementation of the CBS algorithmAppendix A: Self-adjoint differential equationsAppendix B: Non-conservative form of Navier–Stokes equationsAppendix C: Computing drag force and stream functionAppendix D: Convection–diffusion equations: vector-valued variablesAppendix E: Integration formulaeAppendix F: Edge-based finite element formulationAppendix G: Boundary layer–inviscid flow couplingAppendix H: Multigrid methodAppendix I: Mass-weighted averaged turbulence transport equationsAppendix J: Introduction to neural networks