This course considers the fundamental equation of fluid dynamics - the incompressible Navier-Stokes equations. These partial differential equations are nonlinear, not symmetric, and they are a coupled systems of two equations. The dominating term is generally the convective term. All these features lead to difficulties in the numerical simulation of the Navier-Stokes equations. The course will continue the course from the previous semester. Main topics will be the steady-state Navier-Stokes equations, the time-dependent Navier-Stokes equations, and finite element methods for their numerical simulation. Special emphasis will be on the turbulence modeling and the simulation of turbulent flows.
Lecture notes of the first part of this course are available.

Requirements:
Basic knowledge on numerical methods for partial differential equations, in particular finite element methods (Numerical Mathematics 3)

Literatur:
Girault, Vivette; Raviart, Pierre-Arnaud Finite element methods for Navier-Stokes equations. Theory and algorithms. Springer Series in Computational Mathematics, 5. Springer-Verlag, Berlin, 1986.

Layton, William Introduction to the numerical analysis of incompressible viscous flows. With a foreword by Max Gunzburger. Computational Science & Engineering, 6. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2008