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Full 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.
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
