This work develops finite element methods with high order stabilization, and robust and efficient adaptive algorithms for Large Eddy Simulation of turbulent compressible flows. The equations are approximated by continuous piecewise linear functions in space, and the time discretization is done in implicit/explicit fashion: the second order Crank-Nicholson method and third/fourth order explicit Runge-Kutta methods. The full residual of the system and the entropy residual, are used in the construction of the stabilization terms. These methods are consistent for the exact solution, conserves all the quantities, such as mass, momentum and energy, is accurate and very simple to implement. We prove convergence of the method for scalar conservation laws in the case of an implicit scheme. The convergence analysis is based on showing that the approximation is uniformly bounded, weakly consistent with all entropy inequalities, and strongly consistent with the initial data. The convergence of the explicit schemes is tested in numerical examples in 1D, 2D and 3D. To resolve the small scales of the flow, such as turbulence fluctuations, shocks, discontinuities and acoustic waves, the simulation needs very fine meshes. In this thesis, a robust adjoint based adaptive algorithm is developed for the time-dependent compressible Euler/Navier-Stokes equations. The adaptation is driven by the minimization of the error in quantities of interest such as stresses, drag and lift forces, or the mean value of some quantity. The implementation and analysis are validated in computational tests, both with respect to the stabilization and the duality based adaptation. / QC 20110627

The study presented in this thesis investigates the passive exchange of enclosed water with seawater in an offshore wind turbine foundation. This thesis was undertaken in collaboration with Vattenfall R&D, Älvkarleby, Sweden. The water exchange is studied by utilizing Computational Fluid Dynamics (CFD) simulations. A standard monopile foundation, which is installed in Horns Rev 3 wind farm, is considered for the study. The considered geometry consists of two replenishment holes.  The study aims to develop a methodology to utilize CFD simulations to quantify the exchange rate of water. CFD enables studying the effects of different wave parameters and sea states on the economic exchange rate. However, the secondary aim to develop the methodology for the CFD simulations is also to utilize the available computational resources efficiently.  The CFD methodology incorporates the learning from experiments and utilizes a semi-circular domain to enclose the control volume. The results from a mesh sensitivity study establish that a coarser mesh in the domain and a finer mesh within the monopile, coupled with Implicit LES is appropriate to study the overall effect of wave motion on the exchange rate. Also, the additional term scalar transport, incorporated to study the change in concentration within the monopile, provided an appropriate and computationally efficient tool to visualize the variation in water concentration.