Unsteady interface boundary conditions for near-wall turbulence modeling

Abstract

Numerical modeling near-wall turbulent flows is one of major challenges in the fluid dynamics. It inevitably requires significant computational resources. To overcome these difficulties, there are two principal ways based on simplification of the mathematical model and development of ad-hoc computational approaches. The near-wall non-overlapping domain decomposition approach with the use of Robin interface boundary conditions proved to be very efficient. As has been shown, to apply this approach to essentially unsteady flows, the interface boundary conditions must be nonlocal in time and should be modified to include a memory term. In the current paper, it is proven that the memory term must be caused by the unsteadiness of both the solution at the interface boundary and driving force. The properties of the derived unsteady interface boundary conditions are studied in detail in the application to oscillatory and pulsating laminar flows in a channel and pipe. In particular, we study the effect of the memory term on the reproduction of the unsteady effects. The convergence to the exact solution is theoretically proven and numerically demonstrated. A practical calculation of the memory term is based on a Fourier expansion. It is also proven that the convergence is quadratic with respect to the inverse number of Fourier terms. A key question whether the near-wall domain decomposition can damage an external instability plays an important role to identify the perspectives of the technique to be extended to RANS/ LES (or DNS) decompositions.