Data assimilation arises in a vast array of different topics: traditionally in meteorological and oceanographic modelling, wind tunnel or water tunnel experiments and recently from biomedical engineering. Data assimilation is a process for combine measured or observed data with a mathematical model, to obtain estimates of the expected data. The measured data usually contains inaccuracies and is given with low spatial and/or temporal resolution. In this thesis data assimilation for time dependent fluid flow is considered. The flow is assumed to satisfy a given partial differential equation, representing the mathematical model. The problem is to determine the initial state which leads to a flow field which satisfies the flow equation and is close to the given data. In the first part we consider one-dimensional flow governed by Burgers’ equation. We analyze two iterative methods for data assimilation problem for this equation. One of them so called adjoint optimization method, is based on minimization in L2-norm. We show that this minimization problem is ill-posed but the adjoint optimization iterative method is regularizing, and represents the well-known Landweber method in inverse problems. The second method is based on L2-minimization of the gradient. We prove that this problem always has a solution. We present numerical comparisons of these two methods. In the second part three-dimensional inviscid compressible flow represented by the Euler equations is considered. Adjoint technique is used to obtain an explicit formula for the gradient to the optimization problem. The gradient is used in combination with a quasi-Newton method to obtain a solution. The main focus regards the derivation of the adjoint equations with boundary conditions. An existing flow solver EDGE has been modified to solve the adjoint Euler equations and the gradient computations are validated numerically. The proposed iteration method are applied to a test problem where the initial pressure state is reconstructed, for exact data as well as when disturbances in data are present. The numerical convergence and the result are satisfying.

Transonic utter is an aeroelastic instability characterized by part-chord shocks over an airfoil and single mode oscillations leading to a drop in the utter boundary. We present a numerical study that examines the influence of shocks, shock-boundary layer interactions, and three-dimensional flow features on the transonic utter boundary. Using energy concepts we show that shocks and shock-boundary layer interactions have a profound influence on the stability of an aeroelastic system. Viscosity stabilizes the aeroelastic system through thickness effects up-to the bottom of the transonic dip. Beyond, shock induced separation not only stalls the aeroelastic system, but also makes it oscillate about a new equilibrium position. In this region, where viscous effects are dominant, the inviscid utter boundary shows multiple utter points. Modal contributions to the response of the aeroelastic systems |viscous and inviscid | indicate that viscosity restricts higher mode participation. Restriction of higher modes by viscosity is responsible for the elimination of multiple utter points that are present in the inviscid case. Multiple forcing frequencies are observed in those regions of the utter boundary where viscous effects are dominant. Further, the shock dynamics exhibit shock-reversal where-in the shock motion predicted by the viscous simulation is 180_ out of phase relative to that of the inviscid case. At Mach numbers beyond the shock-stall region the shock moves close to the trailing edge of the airfoil, and inviscid and viscous simulations predict almost a similar utter boundary. Three-dimensional transonic flow structures on a finite-span wing aeroelastic model de-stabilizes it relative to an equivalent two-dimensional model.

With steadily increasing computational power, computational fluid dynamics (CFD) can be applied to unsteady problems such as seakeeping simulations. Therefore, a good balance between accuracy and computational speed is required. This thesis investigates the application of CFD to seakeeping performance predictions and aims to propose a best-practice procedure for efficient seakeeping simulations. The widely used KVLCC2 research vessel serves as a test case for this thesis and FINEŠ/Marine software package is used for CFD computations. In order to validate the simulations, results are compared to recent experimental data from SSPA as well as predictions with potential ˛ow code SHIPFLOW® Motions. As for the calm water simulations, both inviscid and viscous ˛ow computations are performed in combination with three mesh refinement levels. Seakeeping simulations with regular head waves of different wavelengths are set-up correspondingly. Furthermore, different strategies for time discretization are investigated. With the given computational resources, it is not feasible to complete seakeeping simulations with a ˝ne mesh. However, already the coarse meshes give good agreement to experiments and SHIPFLOW® Motions' predictions. Viscous ˛ow simulations turn out to be more robust than Euler ˛ow computations and thus should be preferred. Regarding the time discretization, a fixed time discretization of 150 steps per wave period has shown the best balance between accuracy and speed. Based on these findings, a best-practice procedure for seakeeping performance predictions in FINEŠ/Marine is established. Taking the most efficient settings obtained from head wave simulations, the vessel is subjected to oblique waves with 160° encounter angle. Under similar wave conditions, CFD predictions of a similar thesis show close agreement in terms of added wave resistance. Compared to the previous head wave conditions of this study, added resistance in 160° oblique waves is found to be significantly higher. This underlines that oblique bow quartering waves represent a relevant case for determining the maximum required power of a ship. CFD and potential ˛ow show similar accuracy with respect to ship motions and added wave resistance, albeit potential ˛ow outperforms CFD in terms of computational speed. Hence, CFD should be applied in cases where viscous effects are known to have large influence on a vessel's seakeeping behavior. This can be the case if motion control and damping devices are to be evaluated, for instance. / Tack vare den stadigt ökande beräkningskraften kan beräkningsuiddynamik (CFD) idag användas på beräkningsintensiva problem som sjöegenskapssimulationer. Den här rapporten undersöker användning av CFD på sjöegenskapsprestanda och syftar till att foreslå ett best-practice förfaringssätt för effektiv sjöegenskapssimulationer. Forskningsskrovet KVLCC2 fungerar som ett testfall för denna rapport och FINE—/Marine-mjukvarupaketet används för CFD-beräkningar. Viktiga parametrar, såsom ödestyp, beräkningsnät och tidssteg varierars systematiskt. Resultaten jämförs med experiment gjorda vid SSPA. Baserat på resultaten förelås en best-practice. Den föreslagna best-practice användas vidare för berökningar av sjöegenskaper i sneda vågor. Jämförelse av resultaten med liknande studier visar god överensstämmelse. Genom att använda det föreslagna förfarandet för best-practice kan CFD-sjöegenskapssimulationer användas på fall där viskösa krafter måste beaktas, till exempel rörelseregleringsanordningar.