Fluid-Fluid Interaction Problems at High Reynolds Numbers: Reducing the Modeling Error with LES-C

Abstract

We consider a fluid-fluid interaction problem, where two flows (with high Reynolds numbers for one or both of these flows) are coupled through a joint interface. A nonlinear coupling equation, known as the rigid lid condition, creates an extra level of difficulty, typical for atmosphere-ocean problems. We propose a novel turbulence model, NS- -C, from the recently introduced family of LES-C (large eddy simulation with correction) models. Combining it with the so-called geometric averaging (GA) partitioning method, we obtain the NS- -C-GA model that is shown to possess several key properties. First, the preexisting solvers for the subdomains can be used, which is critical, e.g., for atmosphere-ocean applications. Second, the LES-C turbulence models use defect correction to efficiently reduce the modeling error of the corresponding LES models; we demonstrate numerically that the NS- -C model outperforms its LES counterpart, the NS- model. It has also been shown recently that it is favorable for an LES model to have the nonfiltered velocity in the interface terms. The NS- -C-GA model possesses this important property; we also show it to be stable and have optimal convergence properties.