Large Eddy Simulation (LES) is a powerful tool to simulate complex wall-bounded turbulent flows, as it can capture unsteady flow structures and allows for a user-adjustable trade-off between accuracy and computing time: Wall-resolved LES captures the structures of near- wall flow down to the inertial scales and therefore requires a high amount of computing effort; wall-modeled LES replaces the exact equations of motion of the boundary layer flow by a simplified description in terms of wall functions or the turbulent boundary layer equations. Since these models of the turbulent boundary layer can lead to high uncertainty in many flow situations, a new model is proposed in this thesis that covers only the viscous sublayer and parts of the buffer layer. The cubic asymptotic velocity approximation (CAVA) wall model is derived from a cubic Taylor polynomial ansatz for the velocity profile and a linear ansatz for the pressure. Isolating the balances scaling with y 0 and y 1 in the wall distance y from the incompressible Navier-Stokes equations, one can determine the polynomial coefficients. By relating the ansatz functions with the cell averages from LES, one can finally obtain a system of partial differential equations for the wall shear stresses that couples into the LES. For this, the CAVA model requires information from the wall-nearest cells only. It is shown how the proposed model can be integrated with little effort into an existing LES code which employs an explicit time integration scheme. The CAVA model was tested by replacing the coupling terms with their exact values from analytical and numerical solutions of the Navier-Stokes equations and solving for the wall shear stress. For laminar channel flow the model yields the exact solution, while one can obtain at least 3rd order accurate results for the first and second Stokes’ problem and for the Falkner-Skan boundary layer. The accuracy of the CAVA-Model was compared with 1st and 2nd order difference approximations of the wall shear stress for turbulent channel flow at Reτ = 180 and for laminar separating boundary layer flow with varying Reynolds number. The CAVA model yields more accurate results than 1st order difference in all cases and better results than the 2nd order difference in most of the cases, especially for larger cell sizes up to h = 0.4 δ1 in laminar and h+ = 6 in turbulent flow. Further research is required to fully validate the model using highly accurate DNS data and cases of spatially inhomogeneous and unsteady turbulent flow. Moreover, the effects of a two- way coupling between the model and a LES has yet to be investigated. Furthermore, a model developed from the boundary equation shows hints that generalizations of the CAVA model to higher polynomial degrees may be able to capture the growth of the Reynolds stresses with wall distance.     «

Large Eddy Simulation (LES) is a powerful tool to simulate complex wall-bounded turbulent flows, as it can capture unsteady flow structures and allows for a user-adjustable trade-off between accuracy and computing time: Wall-resolved LES captures the structures of near- wall flow down to the inertial scales and therefore requires a high amount of computing effort; wall-modeled LES replaces the exact equations of motion of the boundary layer flow by a simplified description in terms of wall func...     »