[Tobi]

Dear all,

after five weeks hard work during all my spare time for completing the turbulent section, I am done. I really hope that it will help you to understand the things clear. However, yesterday when I re-checked all the stuff, I thought that everything what I did is not understandable. Maybe it was due to the fact that was working with the PDF for more than 10h and the fact that it was 3 am. Don't know.

The new version contains 35 pages more in the topic about turbulence modeling. Furthermore I hope that I discussed everything nice and clear, so that you get the point how to derive all equations in the beauty of crazy mathematics (especially the Reynolds-Stress equation took me 2 weeks to get the point). I hope that one day I get back some fruits of all my voluntaree work

To sum up and not to waste your time, here we go:


Changes from version 2.1 to 3.0

• Extened ~ 35 pages for turbulence modeling

• Correct some mistakes (in general)
• Include the handling of the time derivative as differences first
• English improvements
• Extend and reorganized the mathematic chapter
• Reorganized the chapters
• Reorganize the shear-rate tensor deriviation in OpenFOAM(R)

• Turbulence modeling
  • Introduce to Reynolds-Averaging methods (time-average, ensemble, ...)
  • Time-Averaging operations on linear, nonlinear terms and constants
  • Derivation of incompressible Reynolds time-averaged mass conservation
  • Derivation of compressible Reynolds time-averaged mass conservation (to show why we get more troubles here)
  • Introduce the turbulent Reynolds stress tensor
  • Derivation of incompressible Reynolds time-averaged momentum equation
  • Introducing the closure problem
  • Comparison of Reynolds stress tensor and Cauchy stress tensor (especially to show the modified pressure we use in OpenFOAM p*, important to know in some cases)
  • Introducing to the Boussinesq eddy viscosity approximation
  • Introducing the eddy viscosity approximation
  • Derivation of the incompressible Reynolds-Stress equation to derive the turbulent kinetic energy equation
  • Derivation of the incompressible kinetic energy equation of the turbulence
  • Relation between length scale and dissipation
  • Derivation of the incompressible dissipation rate equation (not shown in detail)

• Introducing the Favre averaging concept
• Demonstrate the concept using the compressible mass conservation equation

As always I would like to receive critiques (bad and good ones), otherwise I can not improve my personal work or know if it is helpful or not. In any case I am really tired now and will open one or more beer(s) now. Cheers.

I decided to declare the new PDF as a book rather than a summary .
My girlfriend has to make a nice cover and then I will print it with a hard cover for myself. After that I will post a nice picture

Sofar... enjoy.


Sources:

http://holzmann-cfd.de/index.php/en/publications

https://www.researchgate.net/profile...n/publications

[Tobi]

Dear all,

at the moment I am revising the book because I am often using it. Therefore, I found a few mistakes that I am going to removed now. Furthermore, the English is improved and a lot of formating will be done in order to formate it to B5 (I will print it for myself). If someone will have a copy of the soft-cover book, feel free to contact me.

[Tobi]

Dear all,

Updates
I spend again 3 weeks evenings to re-organize the book. Therefore, I removed some errors and made improvements of readability. A summary about the changes can be found here: http://holzmann-cfd.de/index.php/de/...s-and-openfoam . Based on the fact that I use the PDF very often and do not like to have PDF's opened on my screen. I will print the book for myself. If someone wish to have a copy of the soft-cover book, just write me an email to tobias.holzmann@holzmann-cfd.de. The new PDF is already available on my website and will be updated on researchgate soon.

Costs
If you are interested in the soft-cover book, you probably want to know the price. I can tell you that I do not want to make money out of it. Based on the amount of books (maybe only the one for me ) the price will reduce but at the moment it seems that it does not matter if I print one to ten. The costs are (at the moment max 10 guys) ~ 30 to 35€ for one book. If we would get 100 people together it can be reduced to round about 12€. I will check if I there are printing companys which prints cheaper (if you know some good source, please let me know). That includes printing and compounding the pages. Of course, you have to add the costs for transport.

I hope this summary will contribute to the open source thought and highlight some important relations and mathematics in general and can clear some points within OpenFOAM.

Contribution
If you want to contribute special topics to the book, you are welcomed! Just contact me.

Critics
Everybody is welcomed to give critical feedback. I am also thinking about implementing the stress calculation and the implemention in OpenFOAM but first I should write my PhD thesis before I am doing anything new now; thesis -> 4 pages ... furthermore there is a book from Tomislav and Jens available and we have the openfoamwiki.

Additional chapter for OpenFOAM planned
Based on the title of the book, it may mislead about the topics. In my opinion, knowing the equations and the mathematics behind is the basic point for manipulating and extending FOAM. During the chapters we also discuss some parts about numerics (especially stabilization), but the book do not discover solving ODE or PDE or discretization that also belong to numerics. However, maybe if I find time, I will add a chapter about OpenFOAM where I discover these parts very briefly and give good literature. If someone would like to have code-snippets for OpenFOAM it might be an option to check out the OpenFOAM Technology Primer book or the openfoam wiki. In any case, my opinion about developing FOAM is the following: if you know c++ in more details, are able to use Doxygen, you can learn FOAM much faster and you are able to manipulate the stuff.


Have a nice day, keep foaming
Tobi

[Tobi]

Dear all,

based on the survey (http://www.cfd-online.com/Forums/ope...tigations.html), one big wish was that I add some description / chapter to the book that is about the PIMPLE algorithm. With 23 new pages, it is done. I am happy to announce the new updated book. All latest updates can be checked out on my website. Here some brief summary:

• Updated chapter 1 (english improvements)
• Updated some equations in chapter 1
• Added missing stuff to chapter 1
• Corrected one literature
• New literature style
• Added hyper ref to the whole document
• New listings for the code part
• Added pressure-momentum coupling algorithm SIMPLE, PISO, PIMPLE
• Added the usage of the PIMPLE algorithm based on a simple example (not the one I used in my blog here: http://www.cfd-online.com/Forums/blo...hm-part-i.html)

You find the PDF on Researchgate or on my website.

PIMPLEasPISOdt2.jpgPIMPLEdtLargeNouter100nCorr2relaxRes.jpgPIMPLEdtLargeNouter5nCorr2.jpg

[Tobi]

Dear all,

I am happy to announce a new update of my book to the final and printable version (4th edition, November). The changes that were made are:

• Cor*rected a lot of typos
• Renewed the intro*duc*tion of the mass con*ser*va*tion equation
• Renewed the intro*duc*tion of the momen*tum con*ser*va*tion equation
• Cor*rected the sum*mary page (equa*tions were wrong)
• Cor*rected equa*tion 2.46
• Improved other equations (added stuff for clearance)
• Added new chap*ter about “Open*FOAM® tutorials”
• Updated and changed a lot of sen*tences for a bet*ter under*stand*ing in the whole documentation
• Added lit*er*a*ture
• Added “how to cite”
• Renewed the abstract
• Book read (for me) to print

If you want to have a soft-cover copy, write me a message. I hope that the work will help you in your research, engineering work or whatever you are going to do with OpenFOAM(R).

Be a part of the community <3!!!
Good night.

[KateEisenhower]

Hi Tobi,

thanks for this great source of information!

A few remarks:
- p. 110: through -> throw
- p. 126: I always use residualControl instead of residualControls as you do. Maybe both of them are possible.
- p. 122: Concerning PIMPLE you write:

As we already mentioned in
section 10.1, the method is not consistent and hence, we are forced to use the underrelaxation
technique.

I think it is not neccessary to use under-relaxation in all cases. Actually I have run pimple cases without any relaxation-factors. Any remarks on this one?

Best regards,

Kate

Addtion: I just checked it. If I use underrelaxation in my transient simulations, it takes considerably longer. Especially if I respect Ferziger's advice

pressure-relaxation-factor+velocity-relaxation-factor = 1

.

[Tobi]

Dear Kate,

thanks for your feedback and your remarks. I am not a perfect guy so I also make mistakes and during the last reviews I removed a lot of typos and especially some equation errors. Lets come to your remarks:

- p. 110: I guess its clear
- p. 126: you are right. I also use residualControl without (s). Don't know why I wrote that. I will remove it (unfortunately I printed my book last week )
- p. 122: Okay, maybe I should add some information:

a) If you use nOuterCorrectors 1, then you probably run in PISO mode and no under-relaxation is needed because the time step is small enough.

b) If you have nOuterCorrectors > 1 you step into PISO + SIMPLE and based on the problem that your are solving, the under-relaxation is needed or not. This depends mainly on your Co number and the stiffness ... if you have coupled systems etc. The outer loops make sure that your explicit sources are converged.

c) if no under relaxation is used and it is running fine, then you are happy and there is no need to do it

d) A real PIMPLE algorithm can take longer but is more accurate. However the advantage of the PIMPLE is to use high Co numbers. I guess that Co = 15 in most cases without under-relaxation will fail.

[RobertHB]

Dear Tobi,

i downloaded your book from Research Gate a few weeks ago because i was looking for a way to improve the models of my MSc. Thesis.
I spend the most of my time with your book reading chapter 10, more precisely 10.4 "The correct usage of the PIMPLE algorithm" and i must say it was/is most usefull. Helped me alot with my own simulations.
The first pages are really beginner friendly and easy to understand. I like your approach of explaining the FVM by starting ground up, really basically with a single volume. I got lost a bit from chapter 2 onward, since i'm missing a lot of mathematical background.
But the introduction and the application/user focused part at the end of your book are really, really helpfull.

Thank you alot for writing this book.

Regards,
Robert

[Tobi]

Dear Robert,

thank you a lot for your feedback. I will check out the chapter 2 and may improve it or add the missing mathematics. I also read e.g. Ferziger & Perić more often because I got lost so many times. The mathematical aspects are really important. The problem is that to understand everything, we should also know stuff about discretization and stuff like that. However, I tried to make it understandable as possible but you know sometimes it is not as easy as you thought and:

a) it was just a private project
b) No review - just me

Maybe in future I will find some contributors to the book to explain more "user-related" stuff. LIke Fumiya is doing in his blog.

Thanks for reading & your feedback.

[RobertHB]

Hello Tobi,

i didn't want to imply that the missing mathematics are your mistake or a weak point of your book. That's a problem at my end and due to a lack of mathematical courses during my studies, basically none.

I'll make sure to check out the book of Ferziger & Perić and Fumiya's blog you pointed out.

Regards
Robert

[Zeppo]

Tobias, Robert, may I recommend you read an exellent book "Moukalled, Mangani, Darwish - The Finite Volume Method in Computational Fluid Dynamics An Advanced Introduction with OpenFOAM® and Matlab (Fluid Mechanics and Its Applications) - 2015". So far I've read nealy 400 pages (out of almost 800 pages in total) and can conclude that this book is one of the most usefull intermediate-level books on CFD. It covers a lot of stuff you need if you want to get familiar with CFD in general and OpenFOAM specifically. I think the book is better than Ferziger-Peric - in writing style, in material presentation, in the way how the authors develop the underlying theory.

Tobias, if somehow you find yourself to be out of ideas on the future topics to cover in your book, please think about writing something about OpenFOAM's internals. For axample, parallel computation and interprocessor communication in OpenFOAM is what I would really like to read about.

[Tobi]

Hi,

as you already suggest this book somewhere in another thread (i think it was something related to upper / lower pointer or matrix construction), I bought it for our chair. I also had some insight which was very useful because there they explain the stuff about pressure velo coupling very nice and matrix construction.

The hint with the processor stuff (boundaries) I already investigated. however, next year I will write my PhD first. After that we will see, how the book will go on

Finally, my book is just a summary of the literature without explaining to much in coding and algorithms.

Nice Christmas to everyone.

Sent from my HTC One mini using CFD Online Forum mobile app

[Tobi]

Dear everybody,

the book is now available in a new version with the following changes:

• A few typos corrected
• One listing updated (residualControls to residualControl)
• Corrected one equation in the shear-rate tensor of the divDevRhoREff section
• Added a chapter about the bulk viscosity
• Based on the bulk viscosity a lot of changes were done in the shear-rate tensor chapter
• Added a chapter about "OpenFOAM Tutorials"

All informations can be found on my website.
As always, download is available on my website and researchgate.

[zordiack]

When I again came across this thread I have to say you have done a great job with that book and kept it going.

I was just enjoying your work when I was double and triple checking my implementations Keep up the good work and if it ever ends up between book covers I promise to buy one

[LuckyTran]

Hi folks, this is a nice thread that I've visited several times in past months while trying to derive perturbed RANS equations, which of course requires that you have the correct governing equations to start with. I don't even use OpenFOAM much, but it was still helpful.

Of course one knows that FVM solvers obviously solve the integral forms of equations, and the conservative forms of equations naturally suit this purpose.

On the equivalency between conservative and non-conservative forms, I think their equivalency is quite subtle. It's not so obvious that they are equivalent except to smoeone already familiar with the mathematics. But for those that are familiar with the mathematics, it is quite easy to forget and it is not-obvious when they are not equivalent. The non-conservative forms are only equivalent to conservative forms only when there are no mass sources/sinks in the continuity equation. One might argue that we never do fusion and never have to worry, but it is a numerical trap because we can never assume continuity to be exactly 0. We can only solve the continuity equation to within a given tolerance.

When most of fluid dynamics was solved analytically, it made sense to go to advective form because there you have nice scalars and vectors and not tensors. It also makes perfect sense to assume continuity will be satisfied, because you are looking for the solution where it is indeed satisfied. Numerically, we cannot do this. Or if we do, we end up wondering what happens to small errors, do they grow or what? Recklessly dropping these terms often results in a numerically unstable solver.

Whereas it is quite obvious that you cannot go from conservative form into the advective-form if you have these mass sources/sinks (you will see plainly that terms do not cancel), it is not so obvious that you cannot go from advective-form to conservative form when you have these sources/sinks (because you cannot see that invisible terms will suddenly appear in the form that you want, because they don't).

I would like to mention that personally, deriving the governing equations in a differential element got me no where. Always you had to know what the end result was because you do not know how the mathematics relates to the physics. In advective form from a differential eleemnt, you really have to scratch your head and ask, what the heck does advection look like mathematically? But to write down the governing equations in conservative form only requires you to know the Reynolds Transport Theorem and to select the property you want to transport: mass, momentum, energy, etc. And only then do you introduce the physical model for fluxes: Fourier's law, Fick's law, Newton-Stokes law, etc. Deriving the governing equations in the non-conservative form from the start requires a lot of hand-waving mathematics because always you have to wonder what is correctly accounted for and what has been modelled and what has been neglected, whereas it is straightforward to write down a transport equation of any conserved quantity and always know exactly what the fluxes are.

So, although I have a personal preference for advective non-conservative forms, I have come to accept that it is an aesthetic preference. The correct equations are always the conservative ones.

[Tobi]

Dear everybody,

I got some feedback and updated the book. The full list of changes are given on my website (Release History):

• Added new chapter about the relaxation methods (field and matrix)
• Corrected typos and equations (9.3 - 9.64)

I still hope that this helps some of you. If you find errors and mistakes, let me know and again - if you want to contribute some special topic, write me.

[Tobi]

Dear everybody,

the book reached 9.000 reads on researchgate and I have registered more than 6.000 downloads from my website. The book is going to be re-formatted during 2018. If one is interested in contributing chapters/sections into the book, contact me via Tobias.Holzmann@Holzmann-cfd.de

Thanks to all people who gave feedback and reported typos/errors. There are still some problems which are not fixed yet. I promise to do in far future

Thanks Bruno for moving my thread into the community contribution sub-forum. I wanted to do exactly the same but saw that it is already there.

[Zeppo]

Hi, Tobias. I remember reading the very first releases of your book some time ago. Now I see it has evolved a lot, you added new stuff and reformatted the old one to some extent. One can see how much hard work has been put into the book. Keep on going!

[Tobi]

Hi all,

I just want to let you know that I updated the book. More information can be found in my website (changes).

Regards,
Tobi

[Tobi]

Hi everybody,


after a long time, I focused on releasing my book to be conform with the latest development line (Foundation version). During the review, various changes were made such as:

• Updated the design
• Corrected typos, wording, and the language
• Added the derivation of the temperature equation for solids
• Renewed the chapter "Calculation of the Shear-Rate Tensor in OpenFOAM®
• Renewed the chapter "The numerical algorithms: SIMPLE, PISO and PIMPLE"
• Split the book in two/three versions
  • Green Free Version Limited - Includes all changes while some pages where faded out
  • Green Paid Version - Includes all changes
  • Blue Paid Version - All new book extensions will be available here (in Progress)
• Rebuild the PIMPLE case and uploaded it to my website

I already updated the PDF's on researchgate and on my website (https://Holzmann-cfd.de).