Bayesian optimization of RANS simulation with Ensemble based Variational method in convergent-divergent channel

This work investigates the applicability of hybrid data assimilation approach to optimize RANS simulation in convergent-divergent channel from perspective of quantifying and reducing the uncertainty of inlet velocity and turbulence model. Specifically, the ensemble based variational method is applied to infer the inlet velocity and turbulent model corrections by assimilating DNS resolutions or limited experimental data. The approach is firstly adopted to infer the inlet velocity profile for the bump and Venturi geometry. The improvement can be achieved at the inlet region for the bump, but for Venturi in light of the limited measurements in APG region, the perturbation of inlet velocity is not sensitive to the observation space. Further the model corrections in k-w SST model are investigated by assimilating the limited sparse experimental data. The improvements can be achieved for both velocity and turbulent kinetic energy(TKE). The results indicate that ensemble based variational method is capable of inferring unknown quantities of both low dimension (D=20) and high dimension (D=2400) with small ensemble size robustly and non-intrusively. This approach can be a good unity for the Bayesian inference or optimization in CFD problems.