Resumen de Development of a large-eddy simulation framework for engineering applications using the finite element method
This thesis develops a large eddy simulation framework for engineering applications using the finite element method. It focuses on the numerical formulation, the wall modelling approach as well as the generation of turbulent inflow conditions, with emphasis on incompressible flows.
A low-dissipation formulation is introduced that uses a non-incremental fractional step method to stabilize the pressure and allow the use of finite element pairs that do not satisfy the inf-sup condition, such as equal order interpolation for velocity and pressure. This stabilization introduces an error of O(dt, h^2) (for linear elements) in the conservation of kinetic energy, while the final scheme preserves momentum and angular momentum. Explicit subgrid scale models are used for turbulent closure. Temporal discretization is performed through an explicit, energy-conserving Runge Kutta scheme, coupled with an eigenvalue-based time step estimator. The formulation is compared with a residual-based Variational Multiscale method in three common benchmark cases: the decaying isotropic turbulence, the Taylor-Green vortex and the turbulent channel flow at Ret = 395, 950 and 2003. Both formulations provide very accurate predictions, however it is observed that for the Variational Multiscale method, the best results are obtained for different values of the stabilization constants, depending on the case and the Reynolds number. On the other hand, the new formulation provides favorable results without any need for ad hoc tuning. The formulation is further evaluated in the flow over a sphere and the flow around an Ahmed body, where very good agreement with the reference DNS data is obtained.
A new approach is introduced for wall modelling in a finite element context. Instead of the classical finite element method, where part of the domain is omitted and the wall model accounts for it, the mesh extends all the way to the wall, as is commonly done in finite differences and finite volumes. The new approach is tested in a turbulent channel flow at Ret = 2003, a neutrally stratified atmospheric boundary layer and the flow over a wall-mounted hump, where it is shown to offer a great improvement over the classical finite element method. The effect of time-averaging the wall model input, as well as moving the exchange interface further away from the wall is also evaluated. In addition, preliminary work is presented on a two-layer non-equilibrium wall model that uses time-averaging to filter the excess Reynolds stresses. It is tested in a turbulent channel flow at Ret = 2003 with accurate results. Significant savings on the computational cost are also achieved by using a wall-model grid that is coarser in the tangential directions, with minimal impact on the results. Furthermore a method of synthesizing turbulent inflow conditions through the diffusion process is compared with a precursor method on the flow over a three-dimensional hill, providing results of similar quality at significantly less computational cost.
Finally, the complete framework is evaluated on the flow around the DrivAer model, a realistic car model developed to facilitate aerodynamic investigations of passenger vehicles, as well as the flow over the Bolund hill, a hill whose geometry represents a scaled-down model of the typical wind farm site. Despite the complexity of the flows and the coarse grids utilized, good agreement with the reference data is achieved.
