Finite Element Method for Fluid Dynamics

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

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• Cálculo diferencial e equações
• Engenharia mecânica
• Mecânica dos fluidos
• Matemática para engenheiros

<p>Reynolds number; large eddy simulation; turbulent flow; shear flow; turbulence; hydrodynamic; velocity measurement; boundary layer; viscoelasticity; boundary layer flow; shock wave; navier-stokes equation</p>