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
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
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
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