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 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
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