Adaptive Large Eddy Simulation and Reduced-Order Modeling

  • S. UllmannEmail author
  • S. Löbig
  • J. Lang
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 1581)


The quality of large eddy simulations can be substantially improved through optimizing the positions of the grid points. LES-specific spatial coordinates are computed using a dynamic mesh moving PDE defined by means of physically motivated design criteria such as equidistributed resolution of turbulent kinetic energy and shear stresses. This moving mesh approach is applied to a three-dimensional flow over periodic hills at Re=10,595 and the numerical results are compared to a highly resolved LES reference solution. Further, the applicability of reduced-order techniques to the context of large eddy simulations is explored. A Galerkin projection of the incompressible Navier–Stokes equations with Smagorinsky sub-grid filtering on a set of reduced basis functions is used to obtain a reduced-order model that contains the dynamics of the LES. As an alternative method, a reduced-order model of the un-filtered equations is calibrated to a set of LES solutions. Both approaches are tested with POD and CVT modes as underlying reduced basis functions.


Large eddy simulation Moving mesh method Reduced-order modeling Adaptivity 



The authors acknowledge the financial support from the German Research Council (DFG) through the SFB568. We would also like to thank Jochen Fröhlich and Claudia Hertel (TU Dresden) for making the turbulent flow solver LESOCC2 available to us and for their kind programming support during our numerical studies.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Center of Smart InterfacesTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Graduate School Computational EngineeringTechnische Universität DarmstadtDarmstadtGermany

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