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We present two different reduced order strategies for incompressibleparameterized Navier-Stokes equations characterized by varying Reynoldsnumbers. The first strategy deals with low Reynolds number (laminar flow) andis based on a stabilized finite element method during the offline stagefollowed by a Galerkin projection on reduced basis spaces generated by a greedyalgorithm. The second methodology is based on a full order finite volumediscretization. The latter methodology will be used for flows with moderate tohigh Reynolds number characterized by turbulent patterns. For the treatment ofthe mentioned turbulent flows at the reduced order level, a new POD-Galerkinapproach is proposed. The new approach takes into consideration thecontribution of the eddy viscosity also during the online stage and is based onthe use of interpolation. The two methodologies are tested on classic benchmarktest cases.

The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows