FVM for Convection Diffusion

This exercise deals with the finite volume discretization of a convection diffusion problem on a 2D nonuniform spatial grid.

The exercise includes

  • implementation of upwind and central difference scheme for the convection term
  • assembling of the system matrices
  • treatment of Neumann and Dirichlet boundaries
  • consistency analysis
  • simulation of the steady and the unsteady problem
  • discussion of consistency and stability
  • numerical estimation of convergence in space and time
  • visualization using paraview

Feel free to download the exercise (PDF) and basic m-files (TAR) for mesh generation and visualization. If you are a tutor, I will be happy to provide you with the complete implementation and example solutions.

BA/MA Theses

Open topics

At the moment I have two topics readily available:

  • Optimal distributed control of linearized Navier-Stokes equations via differential-algebraic matrix Riccati equations
  • Boundary control of cylindric flow using particular Couette-solutions

The projects can be fitted to the needs in terms of complexity, quantity and theory to programming ratio.

Basic knowledge of numerical mathematics and a programming language is mandatory. Knowledge of control theory and fluid dynamics will be useful.

If you are interested, just drop by...

Finished theses

Manuel Baumann, BA (2011): Modellierung und Simulation von Dispersionen in turbulenter Strömung (Modelling and simulation of dispersions in turbulent flow), in German, awarded best BA Thesis 2011 at Department of Math. at TU Berlin
Thesis

Maximilian Behr, MA (2015): Optimierung und Stabilisierung von inkompressiblen Strömungen in M.E.S.S. (Optimization and Stabilization of Incompressible Flow in M.E.S.S), in German, very good MA Thesis at the MPI/OvGU Magdeburg
Thesis Errata

Björn Baran, MA (2016): Optimal control of a Stefan problem with gradient-based methods in FEniCS, very good MA Thesis at the MPI/OvGU Magdeburg

Courses

  • Lecture on Differential Algebraic Equations. See the website for content and notes of the lecture. Summer Term 2016. Otto von Guericke Universität, Magdeburg.
  • Short Course on Model Reduction of Linear Time Invariant Systems. See the website for content and notes of the lecture. Summer 2015. Shanghai University, Shanghai, China.
  • Tutorials for Numerik II (in English with German lecture notes). The lecture notes, exercise sheets and further information are provided on the ISIS-Page. Summer Term 2012. TU Berlin.
  • Exercise accompanying the course Numerik 1 für Ingenieure. Summer Term 2011, TU Berlin.
  • Tutorials for Mathematik für PhysikerInnen IV. Summer Term 2010, TU Berlin.
  • Supervision of a PPM project dealing with modelling and simulation of a boundary layer. See the excellent project report (in German) for details. Winter Term 2009. TU Berlin.

Daily Tips

for working with scipy