The development of computational fluid dynamics has given us a very powerful tool for investigation of fluid dynamics. However, in order to maintain the progress, it is necessary to improve the numerical algorithms. Nowadays, the high-order methods based on the discontinuous projection seem to have the largest potential for the future. In the work, we used open-source framework Nektar++, which provides the high-order discretization method. We tested the abilities of the framework for computing the compressible sonic and transonic flow. We successfully obtained simulations of the viscous and inviscid flow. We computed the lift and the drag coefficients and showed that for a higher polynomial order we can obtain the same accuracy with less degrees of freedom and lower computational time. Also, we tested the shock capturing method for the computation of the inviscid transonic flow and confirmed the potential of the high order methods. 1

This thesis is focused on study of blood flow through the descending aorta using mag- netic resonance imaging and computational hemodynamics. This combination enables simulations of blood flow in patient specific geometries and under various circumstances such as higher heart rate, velocity or blood pressure. The theoretical part describes the governing equations of the blood flow and possible choices of boundary conditions. The weak formulation and discretization in space and time, which leads to the finite element approximation, is presented. The magnetic resonance data is presented in the second part. The process of segmenta- tion is described together with the preparation of the velocity data for comparison with simulation results. Limitations of magnetic resonance imaging are also presented. The developed methodology is one of the contributions of this thesis. The qualitative and quantitative comparison of simulation results and the magnetic res- onance velocity data is presented in the third part. The main result of the thesis is in the comparison of the flow under different wall boundary conditions. The most important finding is that the best fit for the data is the free-slip wall boundary condition, which is the opposite of commonly used no-slip wall boundary condition. 1

Orientador: Cassio Machiaveli Oishi / Banca: Gilcilene Sanchez de Paulo / Banca: Fernando Luiz Pio dos Santos / Resumo: Esta dissertação apresenta uma metodologia para a simulação de escoamentos incompressíveis viscoelásticos não-isotérmicos, onde a viscosidade e o tempo de relaxação do fluido são dependentes da temperatura. A viscoelasticidade do fluido é modelada pelas equações constitutivas Oldroyd-B e PTT (Phan-Thien-Tanner), onde os parâmetros dependentes da temperatura são modelados pela relação WLF (Willians-Landel-Ferry). A metodologia numérica empregada para resolver o modelo não-isotérmico é baseada no método MAC para escoamentos viscoelásticos via método de projeção. Nesta metodologia, as equações de Navier-Stokes e as equações constitutivas Oldroyd-B e PTT são discretizadas pelo método de diferenças finitas em uma malha deslocada. A metodologia foi verificada na simulação do escoamento não-isotérmico bidimensional entre placas paralelas Poiseuille Flow. Finalmente, a metodologia numérica foi aplicada para resolver o problema da contração 4:1, onde são analisados os efeitos das variação de parâmetros na dinâmica dos vórtices. / Abstract: This monograph presents a methodology for simulating non-isothermal viscoelastic incompressible fluid flows where the viscosity and the relaxation time of the fluid are temperature-dependent. The viscoelasticity of the fluid is modeled by the Oldroyd-B and PTT (Phan-Thien-Tanner) models, where the temperature-dependent parameters are modeled by the WLF (Williams-Landel-Ferry) formulation. The numerical methodology used to solve the non-isothermal model is based on the MAC method for viscoelastic fluid flows via projection method. In this methodology, the Navier-Stokes equations and the Oldroyd-B and PTT constitutive equations are discretized by the finite difference method on a staggered grid. The numerical method was verified by simulation two-dimensional non-isothermal Poiseuille flow. Finally, the numerical methodoly was apllied for solving the 4 : 1 contraction problem in order to analyze the influence of parameters on the vortex dynamic. / Mestre

In this thesis, we investigate the stochastic three dimensional Navier-Stokes-∝ model and the stochastic three dimensional Leray-∝ model which arise in the modelling of turbulent flows of fluids. We prove the existence of probabilistic weak solutions for the stochastic three dimensional Navier-Stokes-∝ model. Our model contains nonlinear forcing terms which do not satisfy the Lipschitz conditions. We also discuss the uniqueness. The proof of the existence combines the Galerkin approximation and the compactness method. We also study the asymptotic behavior of weak solutions to the stochastic three dimensional Navier-Stokes-∝ model as ∝ approaches zero in the case of periodic box. Our result provides a new construction of the weak solutions for the stochastic three dimensional Navier-Stokes equations as approximations by sequences of solutions of the stochastic three dimensional Navier-Stokes-∝ model. Finally, we prove the existence and uniqueness of strong solution to the stochastic three dimensional Leray-∝ equations under appropriate conditions on the data. This is achieved by means of the Galerkin approximation combines with the weak convergence methods. We also study the asymptotic behavior of the strong solution as alpha goes to zero. We show that a sequence of strong solution converges in appropriate topologies to weak solutions of the stochastic three dimensional Navier-Stokes equations. All the results in this thesis are new and extend works done by several leading experts in both deterministic and stochastic models of fluid dynamics. / Thesis (PhD)--University of Pretoria, 2010. / Mathematics and Applied Mathematics / unrestricted

This work examines the feasibility of a novel high-order numerical method, which has been termed Flux Correction. It has been given this name because it "corrects" the flux terms of an established numerical method, cancelling various error terms in the fluxes and making the method higher-order. In this work, this change is made to a traditionally second-order finite volume Galerkin method. To accomplish this, higher-order gradients of solution variables, as well as gradients of the fluxes are introduced to the method. Gradients are computed using lagrange interpolations in a fashion reminiscent of Finite Element techniques. For the Euler Equations, Flux Correction is compared against Flux Reconstruction, a derivative of the high-order Discontinuous Galerkin and Spectral Difference methods, both of which are currently popular areas of research in high-order numerical methods. Flux Correction is found to compare favorably in terms of accuracy, and exceeds expectations for convergence rates. For the full Navier-Stokes Equations, the effect of curved elements on Flux Correction are examined. Flux Correction is found to react negatively to curved elements due to the gradient procedure's poor handling of high-aspect ratio elements.

Finite Element computer codes in two and three dimensions were written that solve both laminar and turbulent flow. These codes use the two equation (k and E) turbulence model to evaluate turbulent viscosity. They were tested with 29 different flow problems. The largest two dimensional turbulent problem solved is flow under a sluice gate. A three dimensional vortex flow problem was attempted but was not feasible due to the size of the available computer. The Harwell sparse matrix subroutines of the United Kingdom Atomic Energy Authority were used to solve the set of simultaneous equations. The performance of these subroutines is evaluated. The importance of defining adequate finite element grids and setting proper boundary and initial conditions is discussed.

Dam spillways and downstream areas are used to guide large flows of water during for example heavy rainfall. The large flows give way to turbulent pattern sand velocities that may damage the river banks or the dam structure. Investigation of these water patterns at certain flows are therefore done to examine at risk areas. In this study CFD simulations were performed for different flows with different boundary conditions for varying surface roughness level. Results were then compared to a previous model study from 2009. The ANSYS ecosystem was used in production of the 3D model, construction of mesh and running of simulations.The flow for the maximum discharge capacity of the sluices was simulated as well as the design flow which is the highest flow the dam is supposed to be able to withstand. In this report the flow has been modeled using RANS with the SST kω-model in a VOF transient setup. Results showed that for both the design flow and the maximum discharge capacity flow the energy conversion is functioning poorly and that a considerable backward circulation exists on the right riverside. This behavior could possibly injure the right dam structure by moving debris upwards against the stream.

京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第21151号 / 農博第2277号 / 新制||農||1059(附属図書館) / 学位論文||H30||N5125(農学部図書室) / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 村上 章, 教授 川島 茂人, 教授 藤原 正幸 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

<p>A study has been undertaken to investigate the flow structure in the vicinity of discontinuities in the surface of a high-speed air vehicle. The effect of gaps and steps on aerodynamic heating is of particular interest. The present    thesis presents Reynolds-averaged Navier Stokes  (RANS) calculations of this class of flow. This thesis consists of two studies: a parametric study of cavity flow at Mach 2 and a study to compare with wind tunnel experiments at Mach 6. The calculations for the parametric study used the Menter two-equation SST turbulence model at fully turbulent conditions. These are two-dimensional cavity flows that were carried out to identify the influence of cavity geometry on flow structure and heating distribution inside the cavity, and to categorize cavity flow regimes. The second study employed RANS calculations for conditions  corresponding to Mach 10 wind tunnel experiments carried out by Nestler et al. (AIAA Paper 1968-673) for Mach 6 boundary layer edge conditions. The SST model used in the parametric study was paired with the Menter oneequation transition model and the two-equation realizable κ-ϵ model in CFD++ was used for the computations. The results showed that, even with adjustment of model parameters, the Menter transition model cannot match the location of laminar to turbulent transition, but it demonstrated good agreement with the experimental data in fully turbulent conditions. The two-equation realizable κ-ϵ model, available in CFD++, was able to accurately model transition and showed favorable agreement for fully turbulent conditions as well.</p>

The implementation of a hybrid spectral/finite-element discretization on the unsteady, incompressible, Navier-Stokes equations with a semi-implicit time-stepping method, an explicit treatment of the advective terms, and an implicit treatment of the pressure and viscous terms leads to an algorithm capable of calculating 3D flows over complex 2D geometries. This also results in multiple Fourier mode linear systems which must be solved at every timestep, which naturally leads to two parallelization approaches: Fourier space partitioning, where each processor individually and simultaneously solves a linear system, and physical space partitioning, where all processors collectively solve each linear system, sequentially advancing through Fourier modes. These two parallelization approaches are compared based upon computational cost using multiple solvers: direct sparse LU, smoothed aggregation AMG, and single-level ILUT preconditioned GMRES; and on two supercomputers of different memory architecture(distributed and shared memory). This study revealed Fourier space partitioning outperforms physical space partitioning in all problems analyzed, and scales more efficiently as well. These differences were more dramatic on the distributed memory platform than the shared memory platform. Another study compares the previously mentioned solvers along with one additional solver, pointwise AMG, in Fourier space partitioning without parallelization to better understand computational scaling for problems with large meshes. It was found that the direct sparse LU solver performed well in terms of computational time, scaled linearly, but had very high memory usage which scaled in a super-linear manner. The single-level ILUT preconditioned GMRES solver required the least amount of memory, which also scaled linearly, but only had acceptable performance in terms of computational time for coarse meshes. Both AMG methods scaled linearly in both memory usage and time, and were comparable to the direct sparse LU solver in terms of computational time. The results of these studies are particularly useful for implementation of this algorithm on challenging and complex flows, especially direct numerical and large-eddy simulations. Reducing computational cost allows the analysis and understanding of more flows of practical interest.