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MathematicsNumericsDerivationsAndOpenFOAM.pdf

MathematicsNumericsDerivationsAndOpenFOAM.pdf
File Size:
1.69 MB
Version:
4.0
License:
Author:
Email:
Tobias[dot]Holzmann[at]holzmann-cfd[dot]de
Date:
02 May 2016

Researchgate: https://www.researchgate.net/profile/Tobias_Holzmann/publications

Soft-cover copy can be ordered by senting an email to Tobias.Holzmann@Holzmann-cfd.de

Features

Changes from edition 4 (24.07.2017) to edition 4 (29.07.2017)

  • Page 69, section 9.1the sentence including  "... figure 7.1" was corrected (number of the figure was wrong)
  • Page 70, equation 9.3 corrected
  • Page 86, equation 9.64 corrected
    Thanks to Vigneshwaran Sankar for the hints
  • Page 115, PISO is done with nOuterCorrectors equal one (previous ... equal zero)
    Thanks to Arnav Ajmani for the hint
  • New chapter about the relaxation techniques in OpenFOAM (field and matrix) to get more information about the information loose and the Final flag

 

Changes from edition 4 (21.02.2017) to edition 4 (24.07.2017)

  • Changed the word viscose to viscous (thanks to my colleague Christian Rodrigues)

 

Changes from edition 4 (29.01.2017) to edition 4 (21.02.2017)

  • Changes only related to chapter 7
  • Improved english
  • Added dependency to eqn. 7.4, 7.5, 7.6, 7.7 and 7.8
  • Corrected eqn. 7.16, 7.17 and 7.18

 

Changes from edition 4 (26.11.2016) to edition 4 (29.01.2017)

  • Some typos
  • residualControls changed to residualControl in the chapter of PIMPLE
  • Added chapter about the bulk viscosity
  • Big changes in chapter 4 and 5 according to the bulk viscosity
  • Some sentence correction in chapter 10
  • Corrected equation 10.12
  • Added chapter 12 - OpenFOAM tutorials

 

Changes from version 4 (October 19.10.2016) to edition 4 (26.11.2016)

  • Corrected a lot of typos
  • Renewed the introduction of the mass conservation equation
  • Renewed the introduction of the momentum conservation equation
  • Corrected the summary page (equations were wrong)
  • Corrected equation 2.46
  • Added new chapter about "OpenFOAM(R) tutorials"
  • Updated and changed a lot of sentences for a better understanding in the whole documentation
  • Added literature
  • Added "how to cite"
  • Renewed the abstract
  • Book read (for me) to print

 

Changes from version 4 (October 04.10.2016) to Revision 4 (October 19.10.2016)

  • Added subsection for the usage of the SIMPLEC algorithm
  • Added SIMPLEC to SIMPLE
  • Added SIMPLEC to PIMPLE

 

Changes from version 4 (September) to Revision 4 (October)

  • Implemented english correction in chapter 1 (thanks to Vignesh T.G.)
  • Corrected Gauss summation convention (thanks to Jaap Versteegh)
  • Added non-symmetric tensor definition
  • Extended equation (1.13) to clear some doubts
  • Included hyperref to the document
  • Re-format the code listings
  • New literature style
  • Added a new chapter (23 pages) about the usage of the PIMPLE algorithm (community wish)
  • Some typo correction

 

Changes from version 3 to Revision 4 (September)

  • Corrected figure 2.2
  • Corrected two terms (plus sign of pressure to minus sign)
  • Increased readability drastically
  • Moved Reynolds-Stress equation derivation to the appendix
  • Summary of equation is now a own chapter
  • Changed format to B5 (for book)
  • Generated a book cover
  • Added one literature
  • All formula's are included in the text flow (they end with a point or comma)
  • A lot of equations are new formated



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

 

Changes from version 2.0 to 2.1

  • English improvements and corrections corrected (thanks to Sergei for the nice corrections)
  • Gauss theorem introduced in the mathematic section
  • Equation (1.6) corrected
  • After equation (1.7), the vector notation (brackets) was wrong
  • Equation (1.14) results not in a vector, it results in a scalar
  • Equation (1.15) dyadic sign added
  • Equation (1.16) dyadic sign added
  • Equation (2.4) corrected again
  • The sentence after (2.9) was changed to be more clear
  • Section 2.1.1, remarks and addition information to gauss theorem etc.
  • Equation (2.13) - (2.16) corrected; velocity vector was not bold
  • Literature added for the non-common continuity equation
  • Equation (2.30), (2.31) and (2.32) dyadic sign added
  • Equation (2.77) other re-arrangement, to be more clear what we do
  • Equation (2.78) conversation -> conversion
  • Equation (2.85) 4th term on the RHS is a surface integral (changed integral sign)
  • Added a description why we use the small bullet in the integrals instead of the big bullet (because both represent the inner product of two vectors)
 
 
 
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