The Finite Element Method for Fluid Dynamics

<p>1. The equations of fluid dynamics<br>2. The finite element approximation<br>3. Convection dominated problems – finite element approximations to the convection–diffusion–reaction equation<br>4. Fractional step methods: the characteristic-based split (CBS) algorithm for compressible and incompressible flows<br>5. Incompressible Newtonian laminar flows<br>6. Incompressible non-Newtonian flows<br>7. Free surface flows<br>8. Buoyancy driven flows<br>9. Compressible high-speed gas flow<br>10. Adaptive mesh refinement<br>11. Turbulent flows<br>12. Flow and heat transport in porous media<br>13. Shallow-water problems<br>14. Long and medium waves<br>15. Short waves<br>16. Fluid–structure interaction<br>17. Biofluid dynamics – blood flow<br>18. Data-driven methods<br>19. Computer implementation of the CBS algorithm<br>Appendix A: Self-adjoint differential equations<br>Appendix B: Non-conservative form of Navier–Stokes equations<br>Appendix C: Computing drag force and stream function<br>Appendix D: Convection–diffusion equations: vector-valued variables<br>Appendix E: Integration formulae<br>Appendix F: Edge-based finite element formulation<br>Appendix G: Boundary layer–inviscid flow coupling<br>Appendix H: Multigrid method<br>Appendix I: Mass-weighted averaged turbulence transport equations<br>Appendix J: Introduction to neural networks</p>