## Archive for the ‘**In English**’ Category

## On Ideas and Engineering Education

**Great Ideas:**

Engineering is a collection of great ideas. A good example is the idea of modeling an airfoil by a single point-vortex (lumped vortex method). Knowing the Kutta-Joukowski theorem (or simply following a physical intuition), we conjecture that a vortex is essential to describe a lifting flow, and hope that a flow over a point vortex will provide us with useful information in studying the lift of an airfoil. Then, passion takes over. We struggle to figure out where to place the vortex and how to determine its strength. Finally, we arrive at a remarkable result: a highly accurate lift curve for a thin airfoil over a practical range of angles of attack. A useful tool to analyze and design an airfoil is obtained. I believe that useful engineering tools such as analytical formulas or numerical algorithms have been developed based on ideas and passion of engineers and scientists. An engineering textbook is a collection of stories of great ideas. These wonderful stories inspire students with enthusiasm and excitement, and the spectacular progress in engineering continues.

**Learn with Ideas:**

The above example of a lumped vortex model illustrates an important combination of an idea and passion, or a principle and skills. Ideas are free. Anybody can come up with from anything smart to absurd. But it is not enough. One needs to turn ideas into realities, or simply, to express them: e.g., pictures, novels, songs, equations, etc. Only then can the value of the idea be evaluated. In engineering, to be a great idea, it must yield something useful. For this, skills are required: mathematics, programming, or manufacturing. To learn skills can be boring, but it can be quite exciting if recognized as a means to turn ideas into useful engineering tools or products. Homework can be a good opportunity for students to experience the process of getting ideas to work in engineering applications. For example, they may apply the lumped vortex method to explore tandem airfoils by a pair of vortices or an airfoil in a wind tunnel by the method of mirror images. Through such exercises, students acquire skills as needed and develop an engineering insight. At the same time, these applications will serve as convincing examples that the simple idea of the lumped vortex model is indeed a great idea.

Poor ideas can also be useful in learning. A popular explanation of lift based on a false concept of ‘equal transit time’ and the Bernoulli theorem is a good example. I myself attempted to calculate the lift coefficient of a parabolic airfoil based on this idea, and obtained the result that the lift coefficient at zero angle of attack is proportional to the square of the maximum thickness (See “False Theory of Lift”). The thickness being a small value, the resulting formula significantly underestimates the lift: the lift coefficient is well known from the thin-airfoil theory to be directly proportional to the maximum thickness. It can also be easily proved wrong by experiments. This example shows that there are good ideas and poor ideas in terms of successful engineering applications. Examples of poor ideas are valuable to students who are likely to go through such experiences in future when they deal with real world engineering problems for which the solution cannot be found in textbooks. That is, they can learn how to examine ideas for engineering applications. In this context, it would be a highly educational exercise to let students propose an idea and examine it by themselves.

**Achieve with Ideas:**

Students who have gone through such a learning process are expected to become creative engineers. Given a goal, they would try to come up with ideas and examine them one by one to find the best approach, acquiring skills as needed. In doing so, they continue to strengthen their skills, intuition, and knowledge. A goal of engineering education is to educate such creative engineers and scientists.

Katate Masatsuka

## Comments at LinkedIn 2011

November, 2011

” It led me to some thinking about multigrid. Multigrid can, in principle, achieve grid-independent convergence, the number of multigrid cycles for convergence is the same for any grid size, thus CPU time is simply proportional to the number of unknowns. Suppose optimal and robust multigrid can be implemented for any scheme. Then, doubling the mesh in each direction in 3D will increase CPU time by a factor of 8. It leads me to a 3rd-order scheme that will reduce the solution error by a factor of 8. If we require that these two factors, at least, match each other, we should shoot for 3rd-order schemes, at least, even with the ultimate multigrid solver.”

September, 2011

“The push-button CFD sounds like a training rather than the university education unless it is taught in the context of problem solving. It may be an important skill, but at a university, that is something to be acquired through intellectual activities.”

## Why do I want to post my preprints, notes, and codes in public?

Because I believe it will promote the development of CFD research and education.

There are people who do not have access to journals.

If not impossible, it takes time, money, and an effort to get the paper they get interested in.

The lag it causes, I think, impedes rapid progress in research and education.

At least, I want to make my preprints available to those who come to my website and get interested.

Publishers allow authors to post preprints in public websites:

Authors’ Rights & Responsibilities (Elsevier) –

https://www.elsevier.com/__data/assets/pdf_file/0007/55654/AuthorUserRights.pdf

If people really find it interesting and can get the journal version, they will get it.

To those who think their research do not receive attention as much as they should,

I recommend that they post the preprints and/or place links to the journal versions in thier websites.

There are people who come across your website, get interested in papers in the list of publications,

but couldn’t really get the papers, and give up or just forget it.

I have notes and ideas that have never been promoted to research papers for a long time.

If I just don’t have time to work on them, I’ll keep them until I find time.

But I don’t think that keeping stale notes or stalled ideas for a long time is productive.

I’d share them with anyone who might find them interesting and think they can do something about them.

Also, I would post notes I wrote in understanding other methods and ideas in CFD.

These notes are just personal notes and cannot be research papers, but people may find them useful.

[My CFD notes are posted at http://www.cfdnotes.com .]

I would post my codes that I think are useful (http://cfdbooks.com/cfdcodes.html ).

The code that generates grids and the exact solution to Ringleb’s flow is useful.

Ringleb’s Flow Code (grid generation and exact solution): http://www.cfdbooks.com/cfdcodes/ringleb_v1.f90

This solution has been used by many researchers, but the solution method has always been unexplained.

It should be possible for anyone to write a code, but it takes time and effort and they often won’t/can’t do.

So, I posted my code. Some people have used it for accuracy study and published papers with the results.

Some people wonder how unstructured CFD codes are written.

I provide codes where they can see how the unstructured grid data are generated and stored.

Some people want to know how to write a 1D shock tube code.

I provide an example. I know it is so basic in a particular field, but not necessarily in others.

I try hard to make the code simple enough to understand the algorithms.

If it is hard to understand, it won’t be instructive and won’t serve their intended purpose.

The codes do not need to be efficient and elegant.

Once you understand what is going on, you would probably want to write a better one by yourself.

At that moment, my code has served its purpose.

You might want to ask me “Why then do you sell your book rather than post it in public?”.

I think that a book is different from research papers, notes, and educational codes.

I wanted to know its value.

If no one finds it worth even $9.99 after browsing the preview, it will prove to have no value.