Motivation

The FEAST group has a long tradition in Numerical Analysis (finite element discretizations, multigrid solvers), High Performance Computing and Software Engineering, particularly in Computational Fluid Dynamics (CFD). Our main interest in the last years has been - and still it is - the efficient numerical solution of incompressible flow problems, with a particular emphasis on multidimensional nonstationary flows.

So, we have spent a lot of time with treating the typical difficulties which arise in multidimensional flow simulations, particularly in the fully nonstationary case:

accuracy, robustness and efficiency of the flow solvers flow representation and visualization in 2D and 3D storage medium for dynamic simulation data

The current flow solver is FEATFLOW 1.2 - based on the FEAT2D and FEAT3D packages - which has proven to be an efficient simulation tool. It is included with a comprehensive documentation and all sources. Updates and new versions can always be found at the FEATFLOW homepage.

The current process of generating graphical multimedia output is mainly based on GMV (General Mesh Viewer) and AVS 5/EXPRESS. However, the use of any other sophisticated graphic tool for postprocessing is possible, requiring straightforward modifications only! GMV is freely available for almost all platforms and can be easily applied for the visualization of:

vector fields for velocity-like data scalar data as pressure, streamfunction or temperature isolines, isosurfaces, isovolumes, cutlines, cutplanes dynamic particle tracing etc.

These tools can be used for stationary as well as nonstationary data, and the automatic generation of "videos" is easily supported. The resulting movies (mostly MPEGs) are stored in the "Virtual Album of Fluid Motion" and can be easily accessed under NETSCAPE or similar browsers via Internet.

The resulting "Virtual Album of Fluid Motion" is both a simulation and visualization project for the numerical study of stationary and nonstationary flows in two and three space dimensions which is designed for education and research. Based on its famous predecessor, Van Dyke's "An Album of Fluid Motion", we were motivated to create the computational counterpart, a kind of "Virtual Flow Laboratory".

Hereby, our "Virtual Album of Fluid Motion" is conceptualized in view of several aspects:

	Educational Motivation
	Physical Motivation
	Mathematical Motivation
	"Multimedia Movie Gallery" Motivation

Some last remarks before you may start: The sections "Computational Details" on each page in the Virtual Album contain not only the (more or less) precise definitions of all input parameters, they also include the necessary files and input data which allow to perform the simulation. So, in combination with the FEATFLOW package, all necessary information can be obtained so that the presented flow configuration can be simulated - identically or with further modifications - by everyone!

Please, keep in mind that this Virtual Album was started in 1996, however it is still far from being completed. Nevertheless, we hope to have included a large variety of representative flow types in the current version which can demonstrate the high potential of the FEATFLOW software and which may give a first impression of complex flow simulations!

Anyway, we hope you enjoy the Virtual Album, and we are thankful for all further suggestions!!!

Educational Motivation

The FEATFLOW package has been used for years for education of students coming from Mathematics as well as from Computer Science, Engineering Sciences, Physics and more. As so-called "Software-Praktikum", students in the second or third year can learn to handle modern numerical software in combination with sophisticated graphical and multimedia tools. Moreover, the FEATFLOW package is also the basis for many Diploma, Masters and PhD Thesis and, consequently, part of the student education at many institutes. As supporting multimedia tool, the Virtual Album may help to illustrate abstract mathematical techniques and numerical solution techniques for PDE's, particularly in Computational Fluid Dynamics, and can be employed - with its powerful multimedia components - even in schools to illustrate the facilities of modern Mathematics.

Many examples in the Virtual Album were performed by students, and we particularly emphasize the Section on "Driven Cavity flow" which was completely created by students during the "Software Praktikum" at the University of Heidelberg. Additionally, we recommend the simulations about the influence of wind shields on the drag values for trucks (in "Flow around vehicles") which all have been performed by students at the University of Heidelberg.

Another Software Praktikum in Heidelberg has concentrated on "Flow simulations around some special characters" , mainly to the initials of the participants. The main tasks of such a typical FEATFLOW-Praktikum are to get familiar with the integrated mesh generator DEVISORGRID and with our preferred graphics tool GMV: Both tasks have been successfully solved by most of the students!!!

Physical Motivation

The interested reader may obtain some overview over incompressible flows in very different frameworks. In many simulations, we study the same test configuration for several Reynolds numbers (low, medium up to large) to demonstrate the resulting different flow behaviour.

Moreover, we also play around with different types of inflow configurations and/or changes in the geometrical details to show how "small" differences in the input may lead to very different physical situations.

In that manner, we hope to provide the reader with some "feeling for CFD" based on the existing flow configurations in the Virtual Album, and furthermore we motivate him/her to develop and to examine new configurations. Since all simulations are based on the freely available and included FEATFLOW software, the reader may additionally get an impression about the facilities of this flow solver.

Mathematical Motivation

As an accompanying tool to the specific "printed" literature for the incompressible Navier-Stokes equations, the Virtual Album intends to demonstrate some mathematical problems and possible strategies for improvement in a multimedia-like way. In addition to "usual" tables or plots, we try to exploit the facilities of modern graphical tools to clarify the often somewhat abstract mathematical results about accuracy, robustness and efficiency issues!

We mainly recommend the following flow configurations in the Virtual Album for illustrating typical mathematical problems inside of CFD:

• "Flow around balls, circles, cylinders, etc." for a quantitative examination with respect to spatial and temporal mesh dependencies
• "Flow through a Venturi pipe" for a qualitative and quantitative verification of complex flows in space and time
• "Leapfrogging of smoke rings" for a graphical illustration of numerical boundary conditions

All these graphical demonstrations are thought to be additional examples for the abstract mathematical results of our CFD book!!!

"Multimedia Movie Gallery" Motivation

In addition to all the scientific issues mentioned above, the Virtual Album is simply useful to illustrate our mathematical work in Scientific Computing over the last years with Multimedia-like techniques. As a "colorful" multimedia tool it has been employed in many talks and conference sessions, sometimes far away from any specific scientific background (I confess...:-)

Therefore, in the recent "global village" with Multimedia and Internet for everyone, the Virtual Album can provide all people - who are not numerical experts or CFD specialists - with illustrative information on Computational Fluid Dynamics, since beside their scientific meaning, many flow movies are "beautiful" as they are, and they all together form a "Virtual Art Gallery" based on a fully scientific background!

Thus, the reader may decide why and how to use this Virtual Album and the underlying FEATFLOW software. Anyway, enjoy it and help us with suggestions for future improvements.