Lecture Notes Numerical Methods for Incompressible Flow

The aim of this lecture is to give an overview on modern numerical methods for the computation of incompressible flows. We start with a short introduction to fluid mechanics, including the derivation and discussion of the most important models and equations. The numerical methods discussed in the subsequent part are ordered due to the model they solve, i.e., we start with the stationary Stokes problem, a linear saddle-point problem, then proceed to stationary Navier-Stokes, which adds the complication of a nonlinear equation, and finally discuss the instationary Navier-Stokes equations, which adds time discretizations. In all cases, we shall discuss modern discretization strategies, their major properties, and the solution of the discretized equations. • Basic knowledge of fluid mechanics and associated mathematical models • Discretization of mixed problems and their iterative solution • Modern discretization and iteration methods for the incompressible Navier– Stokes equations • Time integration of instationary Navier–Stokes equations