Interface boundary conditions in near-wall turbulence modeling

Abstract

Near-wall turbulence modeling is a very computationally expensive problem. A new approach suggested here allows us to avoid calculations of the region with high gradients in the vicinity of the wall while retaining sufficient overall accuracy. A non-overlapping domain decomposition is introduced in application to low-Reynolds number RANS models. The domain decomposition is achieved via the transfer of the boundary condition from the wall to an interface boundary. If the governing equations in the inner domain are simplified, then the transmission (interface) boundary conditions are of Robin type. These boundary conditions can be obtained in an analytical form despite the fact that they are nonlinear. Possible ways to achieve a reasonable trade-off between efficiency and accuracy are discussed. The obtained interface boundary conditions are mesh-independent. They can be used to avoid the computationally expensive resolution of a high-gradient region near the wall. Moreover, once the solution is constructed in the outer domain, the near-wall profile can be restored if required. In two extreme cases, if the interface boundary is too close to the wall or too far from it, the so-constructed solution to the problem automatically corresponds to low- and high-Reynolds number models, respectively. It is shown that the new interface boundary conditions are uniformly applicable in a wide range of the interface boundary locations.