Krüger, Torsten: Regularization-based fictitious domain methods. 2012
Inhalt
- Zusammenfassung
- Summary
- Contents
- 1 Introduction
- 2 Description of the model equations
- 2.1 Nomenclature and basic principles
- 2.2 Reaction-Diusion-Convection (RDC) equations
- 2.3 Stokes and Navier-Stokes equations
- 2.4 Fictitious Domain (FD) method
- 2.5 Description of domain geometries
- 3 Discretization
- 3.1 Assumptions on domain and triangulation
- 3.2 FD discretization for the scalar model equation
- 3.3 FD discretization of the Oseen problem
- 3.4 Time discretization
- 4 Numerical treatment
- 4.1 Approximation of the domain and local integration
- 4.2 A geometrical regularization method
- 4.3 Non-linear defect correction
- 4.4 Numerical accuracy
- 5 Applications
- 5.1 Application I: Steady laminar ow around a plain cylinder
- 5.2 Application II: Non-steady ow around a plain cylinder
- 5.3 Application III: Boussinesq equations on multi-connected domains
- 5.4 Application IV: Incompressible viscous flow around a moving plain cylinder
- 6 Discussion and Outlook
- Bibliography