Kriging-enhanced ensemble variational data assimilation for scalar-source identification in turbulent environments

Highlights: • Ensemble variational techniques effectively reconstruct scalar sources in turbulent environments. • Kriging EnVar (KEnVar) enhances the accuracy of reconstruction without additional CFD simulations. • KEnVar outperforms EnVar and adjoint methods at same computational cost. • Optimal sensor placement by minimizing the system condition number. -- Abstract: Various ensemble-based variational (EnVar) data assimilation (DA) techniques are developed to reconstruct the spatial distribution of a scalar source in a turbulent channel flow resolved by direct numerical simulation (DNS). In order to decrease the computational cost of the DA procedure and improve its performance, Kriging-based interpolation is combined with EnVar DA, which enables the consideration of relatively large ensembles with moderate computational resources. The performance of the proposed Kriging-EnVar (KEnVar) DA scheme is assessed and favorably compared to that of standard EnVar and adjoint-based variational DA in various scenarios. Sparse regularization is implemented in the framework of EnVar DA in order to better tackle the case of concentrated scalar emissions. The problem of optimal sensor placement is also addressed, and it is shown that significant improvement in the quality of the reconstructed source can be obtained without supplementary computational cost once the ensemble required by the DA procedure is formed.