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## Section: New Results

### Hybrid FOM/ROM simulations for turbulent flows

We present below results concerning the application of the hybrid FOM/ROM method to a realistic problem in CFD. The purpose of the study is to investigate the behavior of the flow past a car for several front bumper configurations. We here resort to Free-Form Deformation (FFD) based on two parameters to determine a satisfactory parametrization of all possible configurations, and we consider a steady RANS solver at $\mathrm{Re}=4.87·{10}^{6}$ with Spalart-Allmaras turbulence model to simulate the flow. Simulations are performed in collaboration with OPTIMAD (http://www.optimad.it/) exploiting the methodology proposed in [15].

Figure 6 (left) shows the domain decomposition; in the blue region we solve the Full-Order model, while in the outer region we rely on a POD-Galerkin Reduced Order model. The partitioning is obtained adaptively using the algorithm described in [15]. Figure 6 (right) shows the flow prediction error relative to dynamic pressure for the worst-case parameter: the proposed method leads to $2%$ accurate results with a speed-up compared to the full-order model of 8.

Figure 6. hybrid FOM/ROM approach; application to RANS modelling of the flow around a car.