# Mathematics, Numerics, Derivations and OpenFOAM

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 June 4, 2016, 07:53 Book release #41 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Leoben (Austria) Posts: 1,850 Blog Entries: 6 Rep Power: 32 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 modelingIntroduce 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 nsf, jherb, Balzuka and 4 others like this. __________________ Keep foaming, Tobias Holzmann Last edited by Tobi; June 6, 2016 at 04:06.

 August 25, 2016, 05:01 Update #42 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Leoben (Austria) Posts: 1,850 Blog Entries: 6 Rep Power: 32 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. __________________ Keep foaming, Tobias Holzmann

 October 3, 2016, 17:03 #44 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Leoben (Austria) Posts: 1,850 Blog Entries: 6 Rep Power: 32 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 tiam and hunger like this. __________________ Keep foaming, Tobias Holzmann

 November 26, 2016, 19:26 Updated book available #45 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Leoben (Austria) Posts: 1,850 Blog Entries: 6 Rep Power: 32 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*FOAMŪ 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. cedric_duprat, JonW, Dipsomaniac and 1 others like this. __________________ Keep foaming, Tobias Holzmann

 December 15, 2016, 08:41 #46 Senior Member   Join Date: Mar 2015 Posts: 246 Rep Power: 5 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: Code: 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 Code: pressure-relaxation-factor+velocity-relaxation-factor = 1 . Tobi likes this. Last edited by KateEisenhower; December 15, 2016 at 08:51. Reason: Addition

 December 15, 2016, 09:42 #47 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Leoben (Austria) Posts: 1,850 Blog Entries: 6 Rep Power: 32 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. KateEisenhower likes this. __________________ Keep foaming, Tobias Holzmann Last edited by Tobi; December 16, 2016 at 05:51.

 December 21, 2016, 06:09 Much appreaciated #48 New Member   Robert Join Date: May 2015 Posts: 14 Rep Power: 4 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 likes this.

 December 21, 2016, 06:30 #49 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Leoben (Austria) Posts: 1,850 Blog Entries: 6 Rep Power: 32 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. __________________ Keep foaming, Tobias Holzmann

 December 21, 2016, 17:39 #50 New Member   Robert Join Date: May 2015 Posts: 14 Rep Power: 4 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 Tobi likes this.

 December 23, 2016, 14:46 #51 Senior Member     Sergei Join Date: Dec 2009 Posts: 192 Rep Power: 10 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 OpenFOAMŪ 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 and raj kumar saini like this.

 December 23, 2016, 17:06 #52 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Leoben (Austria) Posts: 1,850 Blog Entries: 6 Rep Power: 32 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 raj kumar saini likes this. __________________ Keep foaming, Tobias Holzmann

 January 29, 2017, 05:45 #53 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Leoben (Austria) Posts: 1,850 Blog Entries: 6 Rep Power: 32 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. gkarlsen likes this. __________________ Keep foaming, Tobias Holzmann

 May 17, 2017, 15:45 #54 Member   Pekka Pasanen Join Date: Feb 2012 Location: Finland Posts: 78 Rep Power: 7 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 Tobi likes this.

 July 29, 2017, 09:02 #56 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Leoben (Austria) Posts: 1,850 Blog Entries: 6 Rep Power: 32 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. __________________ Keep foaming, Tobias Holzmann

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