Mesh Adaptation for Computational Fluid Dynamics, Volume 2

Summary of Volume 1

1. Acknowledgments
2. Introduction
3. Chapter 1. CFD Numerical Models
   • 1.1. Compressible flow
     • 1.1.1. Introduction
     • 1.1.2. Spatial representation
     • 1.1.3. Spatial second-order accuracy: MUSCL
     • 1.1.4. Low dissipation advection schemes
     • 1.1.5. Time advancing
     • 1.1.6. Positivity of mixed element-volume formulations
   • 1.2. Viscous compressible flows
     • 1.2.1. Model for laminar flows
     • 1.2.2. Boundary conditions spatial discretization
     • 1.2.3. No-slip boundary condition
     • 1.2.4. Slip boundary condition
     • 1.2.5. Influence stencil
     • 1.2.6. Spalart–Allmaras one equation turbulence model
     • 1.2.7. SA one-equation model without trip and without f_t2 term
     • 1.2.8. “Standard” SA one-equation model (without trip)
     • 1.2.9. “Full” SA one-equation model (with trip)
     • 1.2.10. Mixed element-volume discretization of SA
     • 1.2.11. Implicit time integration
   • 1.3. A multi-fluid incompressible model
     • 1.3.1. Introduction
     • 1.3.2. Bi-fluid incompressible Navier–Stokes equations
     • 1.3.3. Finite element approximation
     • 1.3.4. Error estimate for the level set advection
     • 1.3.5. Provisional conclusion on scheme accuracy
   • 1.4. Appendix: circumcenter cells
     • 1.4.1. Two-dimensional circumcenter cells
     • 1.4.2. Three-dimensional circumcenter cells
   • 1.5. Notes
4. Chapter 2. Mesh Convergence and Barriers
   • 2.1. Introduction
   • 2.2. The early capturing property
     • 2.2.1. Smoothness, non-smoothness, heterogeneity
     • 2.2.2. Behavior of the uniform-mesh strategy
     • 2.2.3. An example of 1D adaptation
   • 2.3. Unstructured meshes in finite element method
     • 2.3.1. Basics ...