Turbulence represents an important phenomenon in fluid dynamics which has to be taken into consideration when simulating problems in Computational Fluid Dynamics (CFD). Several approaches have been introduced for treating turbulence for different discretization techniques at full order level. In this work, we try to address the reduction methodologies which can be used for treating turbulence in the case of parametrized flows in a finite volume setting.

The approaches presented vary from being fully projection-based to hybrid approaches which employ the use of non-intrusive methods for the approximation of certain fluid dynamics variables. The reduction methods involve the usage of the Pressure Poisson Equation (PPE) at reduced order level and the supremizer enrichment approach abbreviated as SUP ROM.

The first two ROMs are called the uniform ROM and the semi-uniform PPE ROM which use only projection methods. The last approach is called hybrid ROM, for which we consider two versions the H-PPE ROM and H-SUP ROM. A comparison of all the ROMs is presented with possible extensions.