Stabilized Finite Element Methods for Computational Fluid Dynamics

All information regarding the lecture and the exercise of the current semester can be found in the respective courses in moodle and TUCaN.

• Part I: Fundamentals, mathematical background and problem statements
  • Prototypical fluid mechanics equations: the advection(-diffusion), Burgers, Stokes and Navier-Stokes equations
  • Relevant components of functional analysis theory
  • Analysis of the model equations with emphasis on the challenges of finite element formulations
• Part II: Solution strategies
  • Stabilized methods; Galerkin least-squares (GLS), artificial diffusion, streamline-upwind Petrov-Galerkin (SUPG)
  • Suitable interpolation pairs in mixed methods (e.g. Taylor-Hood)
  • Discontinuous Galerkin methods
• Part III: Multiscale modeling
  • A short introduction to the physics of turbulence
  • Classical turbulence models: Reynolds-averaged Navier-Stokes (RANS) and large eddy simulation (LES)
  • The variational multiscale method

• Understanding of potential benefits of using the finite element method for flow problems, advanced aspects of finite element theory and challenges that arise when the finite element method is applied to flow problems
• Knowledge of stabilized methods, discontinuous Galerkin formulations and suitable velocity/pressure interpolation pairs
• Basic understanding of turbulence modeling and the variational multiscale method, including some open research questions in this area
• Understanding of the advantages and disadvantages of the finite element method in this context with respect to finite volume methods

Grundlagen der Finite-Elemente-Methode (13-E1-M001) is recommended.