Reducing the modeling error in the fluid-fluid interaction problems with LES-C model

In this study, a numerical method is proposed for a fluid-fluid interaction problem where two flows are coupled through a nonlinear joint interface and one or both of these flows are at high Reynolds numbers. It is known that the nonlinear coupling equation, known as the rigid-lid condition, creates some difficulties for atmosphere-ocean problems. For this interaction problem, a novel turbulence model NS-ω-C is proposed from the family of LES- models. Combining this NS-ω-C model with the Geometric Averaging partitioning method (GA), the NS-ω-C-GA model is obtained, which is shown to have essential numerical properties. First of all, the previous solvers can be used for the subdomains in applications of atmosphere-ocean problems. Furthermore, it is numerically shown that the NS-ω-C model gives better results than the NS-ω model, as LES-C turbulence models use the defect correction approach to efficiently reduce the modeling error of the LES models. It will be proved both theoretically and numerically that the proposed method gives stable results with high accuracy.