The Space Averaged Navier-Stokes Equations and the Commutation Error

  • Volker John
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 34)


To compute the space averaged velocity ū and pressure p̄, equations for these quantities are needed. These equations have to be derived from the governing equations for u and p̄, i.e. from the Navier-Stokes equations. The simple approach consists in applying the filter which defines (ū, p̄) also to the Navier-Stokes equations. Then, under the assumption that differentiation and filtering commute, the basic equations of LES, the space averaged Navier-Stokes equations, are obtained. However, it turns out that an additional modelling step is necessary to derive equations for (ū, p̄) from the space averaged Navier-Stokes equations. This modelling step is discussed in Chapter 4.


Bounded Domain Large Eddy Simulation Strouhal Number Gaussian Filter Filter Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Volker John
    • 1
  1. 1.Institute of Analysis and Numerical Mathematics, Department of MathematicsOtto-von-Guericke-University MagdeburgMagdeburgGermany

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