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Advanced numerical approximations for unstructured finite volume schemes for modeling and simulation of turbulent flows

Ziel

The objective of the proposed research programme would be the development of an unstructured-grid Finite Volume method suitable for the Large Eddy simulation of turbulent flows. The foundation of the proposed research would be an hybrid unstructured grid Finite Volume scheme for 2D and 3D turbulent flows, developed within the host's group. This method is flexible but employs lower-order reconstruction of the dependent variables used in the flux approximations. As a consequence, the accuracy of the method is reasonably adequate for statistical-model calculations, based on the Reynolds averaged Navier-Stokes equations, but not for Large Eddy simulations. The research would focus on the formulation of substantially improved approximations, based on higher-order polynomial reconstructions. High accuracy spatial approximations would be combined with a three-level time approximation to form a fractional time-stepping scheme. The effectiveness of alternative approximations would be examined, ultimately, on the basis of turbulent channel simulations for which highly-resolved reference data have been obtained by using structured-grid Large Eddy simulation within the host's group as part of the EU programme LESFOIL. The proposed research is intended to extend the capabilities of unstructured-grid Finite Volume schemes, so far used for turbulence modeling, to Large Eddy Simulation.

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