Stabilized Finite Element Methods for Computational Fluid Dynamics (FEM III)

Details

Course name Stabilized Finite Element Methods for Computational Fluid Dynamics (FEM III)
Module number 13-E1-M018
TUCaN course number 13-E1-0018-vu (Lecture and exercise)
Lecturer Prof. Dr.-Ing. Dominik Schillinger
Language English
Term Winter
Credit points 6
Examination Oral exam, homework assignments

Contents

Fundamentals mathematical background and problem statements

  • Prototypical fluidmechanics 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

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

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

Remarks

Group exercise

The exercise sessions are integrated into the lecture. Each session is scheduled individually to align with the lecture content and will be announced as early as possible.