Generation of a One-Parameter Family of Residuals for the Filtered Equations of Fluid Motion

  • G. Pantelis
Conference paper
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 54)


Analysis based on Galilean invariance [1] and more recently of positive definiteness [2] are useful in approaching some kind of validation for proposed subgrid scale models used in large eddy simulations. In [3] an attempt is made to construct general formulae for the residual stress-strain in terms of the macroscale variables (equivalently the filtered fields) based on a model error. In [4] it was demonstrated how much formulae could form a template for the discretization scheme and how the differencing coefficients and emperical parameters of the model can be associated. It was suggestive of exploiting the degrees of freedom of the coupled system of emperical and numerical diffrence coefficients to investigate the possible employment of constraints which capture the dominant dissipative-dispersive characteristics of the application. The process also demonstrates how the subgrid scale model can be isolated from the discretization error.


Cauchy Problem Model Error Large Eddy Simulation Subgrid Scale Model Galilean Invariance 
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.
    Speziale, C.G. (1985) Galilean invariance of subgrid-scale stress models in large-eddy simulation of turbulence, J. Fluid Mech., Vol. 156, pp. 55–62ADSzbMATHCrossRefGoogle Scholar
  2. 2.
    Wang, L. (1997) Frame-indifferent and positive-definite Reynolds stress-strain relation, J. Fluid Mech., Vol. 352, pp. 341–358ADSzbMATHCrossRefGoogle Scholar
  3. 3.
    Pantelis, G. (1998) Derivation of macroscale equations for a class of physical applications, Acta Applicandae Mathematicae, Vol. 54, pp. 59–73MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Pantelis, G. (1997) The construction of general structures of large eddy simulation models, in Advances in DNS/LES, C. Liu and Z. Lui (Eds.), Greydon Press, Columbus, pp. 393–400Google Scholar
  5. 5.
    Sobolev, S.L. (1964) Partial Differential Equations of Mathematical Physics, Pergamon PressGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • G. Pantelis
    • 1
  1. 1.Scientific Computing Group, Information Management DivisionA.N.S.T.O.MenaiAustralia

Personalised recommendations