Description
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.- A proven keystone reference in the library for engineers seeking to grasp and implement the finite element method in fluid dynamics- Founded by a prominent pioneer in the field, this eighth edition has been updated by distinguished academics who worked closely with Olgierd C. Zienkiewicz- Includes new chapters on data-driven computational fluid dynamics and independent adaptive mesh and buoyancy driven flow chapters.
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
