Course WI4 011 Computational Fluid Dynamics
6 ECTS points
Course schedule: Second quarter, starting November 7, 2006
Tuesdays 13.45 - 15.30 Lecture room G, EWI building Mekelweg 4
Wednesdays 13.45 - 15.30 Lecture room E, EWI building Mekelweg 4

Examination: oral, upon appointment


Lecture notes: WI4 011 Elements of Computational Fluid Dynamics, by P. Wesseling, are available in the form of a pdf file here.
For a list of errata, click here


MATLAB software is available here in the form of a tar.gz file

Preface to the lecture notes

The technological value of computational fluid dynamics has become undisputed. A capability has been established to compute flows that can be investigated experimentally only at reduced Reynolds numbers, or at greater cost, or not at all, such as the flow around a space vehicle at re-entry, or a loss-of-coolant accident in a nuclear reactor. Large commercial computational fluid dynamics computer codes have arisen, and found widespread use in industry. Users of these codes need to be familiar with the basic principles. It has been observed on numerous occasions, that even simple flows are not correctly predicted by advanced computational fluid dynamics codes, if used without sufficient insight in both the numerics and the physics involved. This course aims to elucidate some basic principles of computational fluid dynamics.
Because the subject is vast we have to confine ourselves here to just a few aspects. A more complete introduction is given in P. Wesseling: Principles of Computational Fluid Dynamics, Springer 2001, and other sources quoted there. Occasionally, we will refer to the literature for further information. But the student will be examined only about material presented in these lecture notes.
Fluid dynamics is governed by partial differential equations. These may be solved numerically by finite difference, finite volume, finite element and spectral methods. In engineering applications, finite difference and finite volume methods are predominant. We will confine ourselves here to finite difference and finite volume methods.
Although most practical flows are turbulent, we restrict ourselves here to laminar flow, because this course is on numerics only. The numerical principles uncovered for the laminar case carry over to the turbulent case. Furthermore, we will discuss only incompressible flow. Considerable attention is given to the convection-diffusion equation, because much can be learned from this simple model about numerical aspects of the Navier-Stokes equations. One chapter is devoted to direct and iterative solution methods.
Errata errata and MATLAB software related to a number of examples discussed in these course notes may be obtained by clicking on the pertaining links above.

Delft, June 2005, P. Wesseling


Table of contents

1. The basic equations of fluid dynamics
2. The stationary convection-diffusion equation in one dimension
3. The stationary convection-diffusion equation in two dimensions
4.The nonstationary convection-diffusion equation
5. The incompressible Navier-Stokes equations
6. Iterative solution methods