We propose a conservative, second-order accurate immersed interface method for representing incompressible fluid flows over complex three dimensional solid obstacles on a staggered Cartesian grid. The method is based on a finite-volume discretization of the incompressible Navier-Stokes equations which is modified locally in cells that are cut by the interface in such a way that accuracy and conservativity are maintained. A level-set technique is used for description and tracking of the interface geometry, so that an extension of the method to moving boundaries and flexible walls is straightforward. Numerical stability is ensured for small cells by a conservative mixing procedure. Discrete conservation and sharp representation of the fluid-solid interface render the method particularly suitable for Large-Eddy Simulations of high-Reynolds number flows. Accuracy, second-order grid convergence and robustness of the method is demonstrated for several test cases: inclined channel flow at Re= 20, flow over a square cylinder at Re= 100, flow over a circular cylinder at Re= 40, Re= 100 and Re= 3900, as well as turbulent channel flow with periodic constrictions at Re= 10,595.@en

We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations. The wall model operates directly on the Cartesian computational mesh without the need for a dual boundary-conforming mesh. The combination of wall model and implicit LES is investigated in detail for turbulent channel flow at friction Reynolds numbers from Re τ = 395 up to Re τ =100,000 on very coarse meshes. The TBLE wall model with implicit LES gives results of better quality than current explicit LES based on eddy viscosity subgrid-scale models with similar wall models. A straightforward formulation of the wall model performs well at moderately large Reynolds numbers. A logarithmic-layer mismatch, observed only at very large Reynolds numbers, is removed by introducing a new structure-based damping function. The performance of the overall approach is assessed for two generic configurations with flow separation: the backward-facing step at Re h = 5,000 and the periodic hill at Re H = 10,595 and Re H = 37,000 on very coarse meshes. The results confirm the observations made for the channel flow with respect to the good prediction quality and indicate that the combination of implicit LES, immersed-interface method, and TBLE-based wall modeling is a viable approach for simulating complex aerodynamic flows at high Reynolds numbers. They also reflect the limitations of TBLE-based wall models.@en

Turbulence modeling and the numerical discretization of the Navier- Stokes equations are strongly coupled in large-eddy simulations. The truncation error of common approximations for the convective terms can outweigh the effect of a physically sound subgrid-scale model. The subject of this thesis is the analysis and the control of local truncation errors in large-eddy simulations. We show that physical reasoning can be incorporated into the design of discretization schemes. Using systematic procedures, a nonlinear discretization method has been developed where numerical and turbulence-theoretical modeling are fully merged. The truncation error itself functions as an implicit turbulence model accurately representing the effects of unresolved scales. Various applications demonstrate the efficiency and reliability of the new method as well as the superiority of an holistic approach.@en

In order to perform Implicit Large Eddy Simulation (ILES) on complex geometries at high Reynolds numbers, a wall model based on the simplified Thin Boundary Layer Equations (TBLE) is designed in the framework of ILES with a cut-cell finite-volume immersed boundary method. This wall model is validated for turbulent channel flow at friction Reynolds number up to Reτ = 2,000 on very coarse grids. The results compared with DNS and LES without wall model show that the wall model has the potential to improve the mean velocity in the outer flow region well at high Reynolds number. The wall model is applied to a complex converging diverging channel flow at Reynolds number Re = 7,900 on very coarse meshes. Improved mean velocities and Reynolds stresses are obtained, which shows that the wall model has the ability to perform ILES on complex geometries at high Reynolds numbers.@en

Recently, the implicit SGS modeling environment provided by the Adaptive Local Deconvolution Method (ALDM) has been extended to Large-Eddy Simulations (LES) of passive-scalar transport. The resulting adaptive advection algorithm has been described and discussed with respect to its numerical and turbulence-theoretical background by Hickel et al., 2007. Results demonstrate that this method allows for reliable predictions of the turbulent transport of passive-scalars in isotropic turbulence and in turbulent channel flow for a wide range of Schmidt numbers. We now intend to use this new method to perform LES of a confined rectangular-jet reactor and compare obtained results to experimental data available in the literature.@en

This work presents an immersed interface method for representing complex boundaries in Implicit Large-Eddy Simulation on three-dimensional, staggered Cartesian Grids. The immersed obstacle in the fluid domain is characterized by a levelset field. Initial flux calculations are carried out for the entire domain in the same way. Cells intersected by the immersed interface then undergo a special treatment: only the fluid part is considered, no-slip condition and no-through-flux condition are imposed by changing the flux balance and a homogeneous Neumann condition for pressure is enforced in the pressure projection. To deal with the small cell problem a cell-mixing procedure is applied. The approach is fully conservative and we demonstrate the method is second-order accurate. The validation and the performance of the approach are done with some numerical examples of 2D and 3D flow configurations.@en

The subgrid-scale (SGS) modeling environment provided by the Adaptive Local Deconvolution Method (ALDM) has been recently extended to Large-Eddy Simulations (LES) of passive-scalar transport. The resulting adaptive advection algorithm has been described and discussed with respect to its numerical and turbulence-theoretical background in Hickel et al. (2007). Results demonstrate that this method allows reliable predictions of the turbulent transport of passive-scalars in isotropic turbulence and in turbulent channel flow from small to moderate Schmidt numbers. Due to the strong influence of the molecular Schmidt number Sc on the Batchelor characteristic scales, difficulties in the modeling of the passive-scalar transport arise when the diffusive structures are several order of magnitude smaller than the viscous scales (Sc 1). In this paper, we present the results from implicit LES of the flow in a confined rectangular-jet reactor and an analysis of the mixing of a passive-scalar with high Schmidt number: Sc = 1, 250. The numerical study is carried out in collaboration with experimentalists from Iowa State University.@en

In order to perform implicit Large Eddy Simulation (LES) of high Reynolds number wall-bounded flows, a wall model based on simplified Thin Boundary Layer Equations (TBLE) is designed and applied to turbulent channel flow for a wide range of friction Reynolds numbers up to Re τ =20,000. The prediction capability of the employed wall model concerning mean velocities and Reynolds stresses is satisfactory, even on very coarse LES grids. The coupling position between the simplified TBLE model and the LES should be located at the bottom of the logarithmic region. The grid resolution requirement depends mainly on the embedded TBLE grids and is only weakly dependent on the Reynolds number.@en

Recently, the implicit SGS modeling environment provided by the Adaptive Local Deconvolution Method (ALDM) has been extended to Large-Eddy Simulations (LES) of passive-scalar transport. The resulting adaptive advection algorithm has been described and discussed with respect to its numerical and turbulence-theoretical background by Hickel et al., 2007. Results demonstrate that this method allows for reliable predictions of the turbulent transport of passive-scalars in isotropic turbulence and in turbulent channel flow for a wide range of Schmidt numbers. We now use this new method to perform LES of a confined rectangular-jet reactor and compare obtained results with experimental data available in the literature.@en