After the retirement of its initiator prof.dr.ir. P. Wesseling (TU Delft), since 2008 the course is presented by dr.ir. M.I. Gerritsma (TU Delft), prof.dr. B. Koren (CWI and TU Delft) and prof.dr. A.E.P. Veldman (University of Groningen). The course is organized as a series of lectures and computer exercises.

The basic model problem is the convection-diffusion equation with dominating convection. A number of spatial discretization methods (non-uniform grids) will be discussed with their pros and cons (upwind/central, lower/higher order, etc.). Also the stability and accuracy of time-integration methods is shortly discussed.

A next step is to study discontinuous solutions of the Euler equations, with focus on the numerical Riemann problem. Several numerical schemes for calculating shocks and contact-discontinuities will be presented; the concept of non-linear limiters is introduced. The theory is illustrated by calculations of complex shock patterns (e.g. through bubbles).

Also, the incompressible Navier-Stokes equations are discussed. The positioning of the computational grid is assessed (staggered grids), as well as the treatment of boundary conditions. Emphasis is on the role of the pressure. An application is the direct numerical simulation of turbulent flow.

Gerritsma (2008) | lecture notes | exercises | files-exercise1, files-exercise2 |

Koren (2008) | lecture notes | exercises | exercise-files |

Veldman (2014) | lecture notes | exercise-files (*.tar) ,
exercise-files (*.zip) | presentation on DNS
DNS blokje Re=22000 interactive grid: CDgrafisch.m, CDteken.m |