Adaptive Large Eddy Simulation and Reduced-Order Modeling
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.
KeywordsLarge 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.
- 2.Hertel, C., Schümichen, M., Löbig, S., Fröhlich, J., Lang, J.: Adaptive large eddy simulation with moving grids. Preprint Technische Universität Dresden, accepted for publication in Theoretical and Computational Fluid Dynamics (2012)Google Scholar
- 4.Ullmann, S., Lang, J.: A POD-Galerkin reduced model with updated coefficients for Smagorinsky LES. In: Pereira, J.C.F., Sequeira, A., Pereira, J.M.C. (eds) Proceedings of the V European Conference on Computational Fluid Dynamics ECCOMAS CFD 2010, Lisbon, Portugal (2010)Google Scholar
- 5.Erdmann, B., Lang, J., Roitzsch, R.: Kardos user’s guide. ZIB-Report 02–42, ZIB (2002)Google Scholar
- 6.Lang, J.: Adaptive incompressible flow computations with linearly implicit time discretization and stabilized finite elements. In: Papailiou, K., Tsahalis, D., Periaux, J., Hirsch, C., Pandolfi, M. (eds.) Computational Fluid Dynamics ’98. Chichester, New York (1998)Google Scholar
- 9.Hertel, C., Fröhlich, J.: Error reduction in LES via adaptive moving grids, QLES II, Pisa, Italien. In: M.-V. Salvetti et al. (Hsg.) Proceedings: Quality and Reliability of Large-Eddy Simulations II, Springer, 9–11 September 2009Google Scholar
- 22.van Dam, A.: Go with the flow. In: Ph.D. Thesis, Utrecht University (2009)Google Scholar