We prove a global-in-time and large-data existence of a suitable weak solution to a system of partial differential equations describing an unsteady flow of homogeneous incom- pressible viscoelastic rate-type fluid. The material parameters are continuous functions of temperature and, in particular, the dependence of the shear modulus is assumed to be linear. It is shown that studied models obey the fundamental laws of thermodynamics. The key step towards the existence proof is derivation of the balance of entropy. This in- equality is paramount in the analysis and as its consequence, we obtain sufficient a priori estimates, positivity of temperature and also regularity of the elastic deformation. The second part of the thesis deals with the existence analysis for the isothermal case, however using a completely different method, which is of independent interest. 1

Numerical solutions of the Navier-Stokes Equations became more popular in recent decades with increasingly accessible and powerful computational resources. Simulations in reconstructed or artificial pore geometries are often performed to gain insight into microscopic fluid flow structures or are used for upscaling quantities of interest, like hydraulic conductivity. A physically adequate representation of pore-scale flow fields requires analysis of large domains. We solve the incompressible NSE in artificial ordered and random pore-space structures. A simple cubic and face-centred packings of spheres placed in a square duct are analysed. For the fluid flow simulations of random media, packings of spheres, icosahedra, and cubes forming unconsolidated sediments are generated using a rigid body simulation software. The Direct Numerical Simulation method is used for the solution of the NSE implemented in the open-source computational fluid dynamics software OpenFOAM. The influence of the number of spheres in ordered packings, the mesh type, and the mesh resolution is investigated for fluid flow up to Reynolds numbers of 100 based on the spheres' diameter. The random media mesh generation method relies on approximate surface reconstruction. The resulting tetrahedral meshes are then used for steady-state simulations and refined based on an a-posteriori error estimator. The fluid flow simulation results can further be used twofold: 1) They provide homogenized hydro-mechanical properties of the analysed medium for the larger meso and macro groundwater flow simulations. A concept of one-way binding for large-scale simulations is presented. 2) Visualisation: A post-processing image rendering technique was employed in interactive and still image visualisation environments allowing better overview over local fluid flow structures. The ogs FEM code for the solution of large-scale groundwater processes was inspected for computational efficiency. The conclusions drawn from this analysis formed the~basis for the implementation of the~new version of the code---ogs6. The improvements include comparison of linear algebra software realisations and an implementation of optimized memory access patterns in FEM-local assembler part.

Cette thèse est consacrée à l'analyse mathématique et numérique d'un problème d'interaction fluide-structure stationnaire, couplant un fluide newtonien, visqueux et incompressible, modélisé par les équations de Stokes 2D et une structure déformable, décrite par les équations d'une poutre 1D. Le fluide et la structure sont couplés via une condition aux limites de type frottement à l'interface.Dans l'étude théorique, nous montrons un résultat d'existence et unicité de solutions faibles, dans le cadre de petits déplacements, du problème de couplage fluide structure avec une condition de glissement de type Tresca en utilisant le théorème de point fixe de Schauder.Dans l'analyse numérique, nous étudions d'abord, l'approximation du problème de Stokes avec la condition de Tresca par une méthode d'éléments finis mixtes à quatre champs. Nous montrons ensuite une estimation d'erreur a priori optimale pour des données régulières et nous réalisons des tests numériques. Enfin, nous présentons un algorithme de point fixe pour la simulation numérique du problème couplé avec des conditions aux limites non linéaires. / This PHD thesis is devoted to the theoretical and numerical analysis of a stationary fluid-structure interaction problem between an incompressible viscous Newtonian fluid, modeled by the 2D Stokes equations, and a deformable structure modeled by the 1D beam equations.The fluid and structure are coupled via a friction boundary condition at the fluid-structure interface.In the theoretical study, we prove the existence of a unique weak solution, under small displacements, of the fluid-structure interaction problem under a slip boundary condition of friction type (SBCF) by using Schauder fixed point theorem.In the numerical analysis, we first study a mixed finite element approximation of the Stokes equations under SBCF.We also prove an optimal a priori error estimate for regular data and we provide numerical examples.Finally, we present a fixed point algorithm for numerical simulation of the coupled problem under nonlinear boundary conditions.

In this report the regular finite differences method (FDM) and a least-squares radial basis function-generated finite differences method (RBF-FD-LS) is used to solve the two-dimensional incompressible Navier-Stokes equations for the lid driven cavity problem. The Navier-Stokes equations is solved using stream function-vorticity formulation. The purpose of the report is to compare FDM and RBF-FD-LS with respect to accuracy and computational cost. Both methods were implemented in MATLAB and the problem was solved for Reynolds numbers equal to 100, 400 and 1000. In the report we present the solutions obtained as well as the results from the comparison. The results are discussed and conclusions are drawn. We came to the conclusion that RBF-FD-LS is more accurate when the stepsize of the grids used is held constant, while RBF-FD-LS costs more than FDM for similar accuracy.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第19677号 / 工博第4132号 / 新制||工||1638(附属図書館) / 32713 / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 五十嵐 晃, 准教授 米山 望, 准教授 森 信人 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Ocean noise pollution is an invisible but growing threat. There are many sources of sound in the ocean but human underwater radiated noise, in particular from shipping is one of the most prominent one. Ocean noise pollution can interfere or sometimes even directly harm marine life.  This thesis is in collaboration with Kongsberg Maritime which aims to develop an underwater radiated noise prediction method for the ELegance pod system. In particular, the focus is on the noise generated as a direct effect of the permanent magnet motor vibrations. Kongsberg wants to be able to calculate the underwater radiated noise for different pod geometries and engine configurations in order to find an optimal operating speed of the electric motor. The underwater radiated noise prediction is carried out using two methods. The first one is a 2-way coupled fluid-structure interaction harmonic response model, dealing with the vibrations. In addition, the flow induced noise is evaluated using CFD combined with Ffowcs-Williams Hawkings acoustic analogy.  The harmonic response model is used to calculate the sound in terms of a frequency response, which can be translated to revolutions per minute of the rotor. This allows Kongsberg to identify rotor speeds where the operation may or may not be optimal. The flow induced noise is investigated for a typical transit speed. The results show this noise is multiple orders of magnitude smaller than the sound caused by the vibrations. This together with the fact that the computational cost of CFD is large suggests that the flow induced noise is not something Kongsberg needs to consider at an early design stage. Neither the propeller nor cavitation is considered in this thesis, due to the limited computational resources but also that Kongsberg designs propellers that are vessel specific. These sources of sound become important when considering the full acoustic profile of a propulsion unit of this type.

Climate change is an evermore urging existential treat to the human enterprise. Mean temperature and greenhouse gas emissions have in-creased exponentially since the industrial revolution. But solutions are also mushrooming with exponential pace. Renewable energy technologies, such as wind and solar power, are deployed like never before and their costs have decreased significantly. In order to allow for further transformation of the energy system these technologies must be refined and optimised. In wind energy one important field with high potential of refinement is aerodynamics. The aerodynamics of wind turbines constitutes one challenging research frontier in aerodynamics today.   In this study, a novel approach for calculating wind turbine flow is developed. The approach is based on the partially parabolic Navier-Stokes equations, which can be solved computationally with higher efficiency as compared to the fully elliptic version. The modelling of wind turbine thrust is done using actuator-disk theory and the torque is modelled by application of the Joukowsky rotor. A validation of the developed model and force implementation is conducted using four different validation cases.   In order to provide value for industrial wind energy projects, the model must be extended to account for turbulence (and terrain in case of onshore projects). Possible candidates for turbulence modelling are parabolic k-ε and explicit Reynolds stress turbulence models. The terrain could possibly be incorporated consistently with the used projection method by altering the finite difference grid layout.

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Apesar de as EDPS que modelam leis de conservação e problemas em dinâmica dos fluídos serem bem estabelecidas, suas soluções numéricas continuam ainda desafiadoras. Em particular, há dois desafios associados à computação e ao entendimento desses problemas: um deles é a formação de descontinuidades (choques) e o outro é o fenômeno turbulência. Ambos os desafios podem ser atribuídos ao tratamento dos termos advectivos não lineares nessas equações de transporte. Dentro deste canário, esta tese apresenta o estudo do desenvolvimento de um novo esquema \"upwind\" de alta resolução e sua associação com modelagem da turbulência. O desempenho do esquema é investigado nas soluções da equação de advecção 1D com dados iniciais descontínuos e de problemas de Riemann 1D para as equações de Burgers, Euler e águas rasas. Além disso, são apresentados resultados numéricos de escoamentos incompressíveis 2D e 3D no regime laminar a altos números de Reynolds. O novo esquema é então associado à modelagem \'capa\' - \'epsilon\' da turbulência para a simulação numérica de escoamentos incompressíveis turbulentos 2D e 3D com superfícies livres móveis. Aplicação, verificação e validação dos métodos numéricos são também fornecidas / Althought the PDEs that model conservation laws and fluid dynamics problems are well established, their numerical solutions have presented a continuing challenge. In particular, there are two challenges associated with the computation and the understanding of these problems, namely, formation of shocks and turbulence. Both challenges can be attributed to the nonlinear advection terms of these transport equations. In this scenario, this thesis presents the study of the development of a new high-resolution upwind scheme and its association with turbulence modelling. The performance of the scheme is investigated by solving the 1D advection equation with discontinuous initial data 1D Riemann problems for Burgers, Euler and shallow water equations. Besides, numerical results for 2D and 3D incompressible laminar flows at high Reynolds number are presented. The new scheme is then associated with the \'capa - \' epsilon\' turbulence model for the simulation of 2D and 3D incompressible turbulent flows with moving free surfaces. Application, verification and validation of the numerical methods are also provided