Numerical Errors in CFD and DEM Modeling

  • Jon Elvar Wallevik
  • Knut Krenzer
  • Jörg-Henry Schwabe
Part of the RILEM State-of-the-Art Reports book series (RILEM State Art Reports, volume 15)


Numerical error present in Computational Fluid Dynamics (CFD) is given in Chapters 4.1. to 4.6. In the last chapter of this document, Chapter 4.7, a special attention is given to the error present for the Discrete Element Method (DEM). However, it should be clear that much of the topic present in Chapters 4.1 to 4.6 applies also for DEM, and other numerical flow techniques not mentioned here.


Shear Rate Computational Fluid Dynamics Numerical Error Grid Refinement Cement Base Material 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    AIAA, Guide for the Certification and Validation of Computational Fluid Dynamics Simulations. AIAA Guide G-077-1998 (1998)Google Scholar
  2. 2.
    Casey, M., Wintergerste, T. (eds.): ERCOFTAC (2000), Best Practice Guidelines, Version 1.0. ERCOFTAC Special Interest Group on Quality and Trust Industrial CFD (2000)Google Scholar
  3. 3.
    Versteeg, H.K., Malalasekera, W.: An introduction to computational fluid dynamics – the finite volume method, 2nd edn. Pearson Education Limited, England (2007)Google Scholar
  4. 4.
    Oberkampf, W.L., Trucano, T.G.: Verification and Validation in Computational Fluid Dynamics. Prog. Aerosp. Sci. 38, 209–272 (2002)CrossRefGoogle Scholar
  5. 5.
    Mase, G.E.: Schaums Outline Series: Theory and Problems of Continuum Mechanics. McGraw–Hill Inc., USA (1970)Google Scholar
  6. 6.
    Malvern, L.E.: Introduction to the Mechanics of Continuous Medium. Prentice-Hall Inc., New Jersey (1969)Google Scholar
  7. 7.
    Edwards Jr., C.H., Penney, D.E.: Calculus and Analytical Geometry, 2nd edn. Prentice-Hall, Inc., USA (1986)Google Scholar
  8. 8.
    Langtangen, H.P.: Computational Partial Differential Equations, Numerical Methods and Diffpack Programming. Lecture Notes in Computational Science and Engineering. Springer, Berlin (1999)zbMATHGoogle Scholar
  9. 9.
    Wallevik, J.E.: Rheology of Particle Suspensions - Fresh Concrete, Mortar and Cement Paste with Various Types of Lignosulfonates (Ph.D.-thesis); Department of Structural Engineering, The Norwegian University of Science and Technology (2003), ISBN 82-471-5566-4, ISSN 0809-103X
  10. 10.
    Kolman, B.: Introductory linear algebra with applications, 5th edn. Maxwell Macmillan International (1993)Google Scholar
  11. 11.
    Wallevik, J.E.: Minimizing end–effects in the coaxial cylinders viscometer: Viscoplastic flow inside the ConTec BML Viscometer 3. J. Non-Newtonian Fluid Mech. 155, 116–123 (2008)CrossRefzbMATHGoogle Scholar
  12. 12.
    Anderson, J.D.: Computational Fluid Dynamics, The Basics with Applications. McGraw-Hill, Inc., USA (1995)Google Scholar
  13. 13.
    Fletcher, C.A.J.: Computational Techniques for Fluid Dynamics, 2nd edn. Springer Series in Computational Physics, vol. I. Springer, Germany (1990)Google Scholar
  14. 14.
    Tattersall, G.H., Bloomer, S.J.: Further development of the two–point test for workability and extension of its range. Mag. Concr. Res. 31(109), 202–210 (1979)CrossRefGoogle Scholar
  15. 15.
    Tattersall, G.H., Banfill, P.F.G.: The Rheology of Fresh Concrete. Pitman Books Limited, Great Britain (1983)Google Scholar
  16. 16.
    Tattersall, G.H.: Workability and Quality Control of Concrete. E & FN Spon, Great Britain (1991)Google Scholar
  17. 17.
    Domone, P.L.J., Yongmo, X., Banfill, P.F.G.: Developments of the two–point workability test for high–performance concrete. Mag. Concr. Res. 51(3), 171–179 (1999)CrossRefGoogle Scholar
  18. 18.
    Wallevik, J.E.: Rheological properties of cement paste: thixotropic behavior and structural breakdown. Cement Concr. Res. 39, 14–29 (2009)CrossRefGoogle Scholar
  19. 19.
    Oldroyd, J.G.: A Rational Formulation of the Equations of Plastic Flow for a Bingham Solid. Proc. Camb. Philos. Soc. 43, 100–105 (1947)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Oldroyd, J.G.: Two-Dimensional Plastic Flow of a Bingham Solid. Proc. Camb. Philos. Soc. 43, 383–395 (1947)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Barnes, H.A., Hutton, J.F., Walters, K.: An Introduction to Rheology. Elsevier Science, Amsterdam (1989)Google Scholar
  22. 22.
    Irgens, F.: Continuum Mechanics. Springer, Berlin (2008)Google Scholar
  23. 23.
    Tanner, R.I., Walters, K.: Rheology: An Historical Perspective. Elsevier Science B.V., Netherlands (1998)Google Scholar
  24. 24.
    Bercovier, M., Engelman, M.: A finite element method for incompressible non–Newtonian flows. J. Comput. Phys. 36, 313–326 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Taylor, A.J., Wilson, S.D.R.: Conduit flow of an incompressible, yield–stress fluid. J. Rheol. 41(1), 93–101 (1997)CrossRefGoogle Scholar
  26. 26.
    Burgos, G.R., Alexandrou, A.N., Entov, V.: On the determination of yield surfaces in Herschel–Bulkley fluids. J. Rheol. 43(3), 463–483 (1999)CrossRefGoogle Scholar
  27. 27.
    Papanastasiou, T.C.: Flow of material with yield. J. Rheol. 31, 385–404 (1987)CrossRefzbMATHGoogle Scholar
  28. 28.
    O’Donovan, E.J., Tanner, R.I.: Numerical study of the Bingham squeeze film problem. J. Non-Newtoninan Fluid Mech. 15, 75–83 (1984)CrossRefzbMATHGoogle Scholar
  29. 29.
    Wallevik, J.E.: Development of Parallel Plate-Based Measuring System for the ConTec Viscometer. In: Proceedings of the 3rd International RILEM Symposium on Rheology of Cement Suspensions such as Fresh Concrete, August 19-21, RILEM Publications S.A.R.L., Reykjavik (2009) ISBN: 978-2-35158-091-2Google Scholar

Copyright information

© RILEM 2014

Authors and Affiliations

  • Jon Elvar Wallevik
    • 1
  • Knut Krenzer
    • 2
  • Jörg-Henry Schwabe
    • 3
  1. 1.ICI RheocenterInnovation Center IcelandReykjavíkIceland
  2. 2.Institut für Fertigteiltechnik und Fertigbau Weimar e.V.WeimarGermany
  3. 3.University of Applied Science JenaJenaGermany

Personalised recommendations