A numerical method (SIMPLE DIRK Method) for unsteady incompressible viscous flow simulation is presented. The proposed method can be used to achieve arbitrarily high order of accuracy in time-discretization which is otherwise limited to second order in majority of the currently used simulation techniques. A special class of implicit Runge-Kutta methods is used for time discretization in conjunction with finite volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field in a lid-driven square cavity. In the test case calculations, power law scheme was used in spatial discretization and time discretization was performed using a second-order implicit Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was obtained from the proposed method and compared with that obtained from a commercial computational fluid dynamics software program, FLUENT 6.2.16. Also, steady state solution from the present method was compared with the numerical solution of Ghia, Ghia, and Shin and that of Erturk, Corke, and Goökçöl. Good agreement of the solution of the proposed method with the solutions of FLUENT; Ghia, Ghia, and Shin; and Erturk, Corke, and Goökçöl establishes the feasibility of the proposed method.

We connect the Mimetic Finite Difference method (MFD) with the finite-volume two-point flux scheme (TPFA) for Voronoi meshes. The main effect is reducing the saddle-point system to a much smaller symmetric-positive definite matrix. In addition, the generalization allows MFD to seamlessly integrate with existing porous media modeling technology. The generalization also imparts the monotonicity property of the TPFA method on MFD. The connection is achieved by altering the consistency condition of the velocity bilinear operator. First-order convergence theory is presented as well as numerical results that support the claims. We demonstrate a methodology for using MFD in modeling fluid flow in fractures coupled with a reservoir. The method can be used for nonplanar fractures. We use the method to demonstrate the effects of fracture curvature on single-phase and multi-phase flows. Standard benchmarks are used to demonstrate the accuracy of the method. The approach is coupled with existing reservoir simulation technology. / text

In this manuscript, three main contributions are illustrated concerning the propagation and the analysis of uncertainty for computational fluid dynamics (CFD) applications. First, two novel numerical schemes are proposed : one based on a collocation approach, and the other one based on a finite volume like representation in the stochastic space. In both the approaches, the key element is the introduction of anon-linear multiresolution representation in the stochastic space. The aim is twofold : reducing the dimensionality of the discrete solution and applying a time-dependent refinement/coarsening procedure in the combined physical/stochastic space. Finally, an innovative strategy, based on variance-based analysis, is proposed for handling problems with a moderate large number of uncertainties in the context of the robust design optimization. Aiming to make more robust this novel optimization strategies, the common ANOVA-like approach is also extended to high-order central moments (up to fourth order). The new approach is more robust, with respect to the original variance-based one, since the analysis relies on new sensitivity indexes associated to a more complete statistic description.

A three-dimensional, parallel, anisotropic, block-based, adaptive mesh refinement (AMR) algorithm is proposed and described for the solution of fluid flows on body-fitted, multi-block, hexahedral meshes. Refinement and de-refinement in any grid block computational direction, or combination of directions, allows the mesh to rapidly adapt to anisotropic flow features such as shocks, boundary layers, or flame fronts, common to complex flow physics. Anisotropic refinements and an efficient and highly scalable parallel implementation lead to a potential for significant reduction in computational cost as compared to a more typical isotropic approach. Unstructured root-block topology allows for greater flexibility in the treatment of complex geometries. The AMR algorithm is coupled with an upwind finite-volume scheme for the solution of the Euler equations governing inviscid, compressible, gaseous flow. Steady-state and time varying, three-dimensional, flow problems are investigated for various geometries, including the cubed-sphere mesh.

A three-dimensional, parallel, anisotropic, block-based, adaptive mesh refinement (AMR) algorithm is proposed and described for the solution of fluid flows on body-fitted, multi-block, hexahedral meshes. Refinement and de-refinement in any grid block computational direction, or combination of directions, allows the mesh to rapidly adapt to anisotropic flow features such as shocks, boundary layers, or flame fronts, common to complex flow physics. Anisotropic refinements and an efficient and highly scalable parallel implementation lead to a potential for significant reduction in computational cost as compared to a more typical isotropic approach. Unstructured root-block topology allows for greater flexibility in the treatment of complex geometries. The AMR algorithm is coupled with an upwind finite-volume scheme for the solution of the Euler equations governing inviscid, compressible, gaseous flow. Steady-state and time varying, three-dimensional, flow problems are investigated for various geometries, including the cubed-sphere mesh.

Gradient-based aerodynamic shape optimization, based on Computational Fluid Dynamics analysis of the flow, is a method that can automatically improve designs of aircraft components. The prospect is to reduce a cost function that reflects aerodynamic performances. When the shape is described by a large number of parameters, the calculation of one gradient of the cost function is only feasible by recourse to techniques that are derived from the theory of optimal control. In order to obtain the best computational efficiency, the so called adjoint method is applied here on the complete mapping, from the parameters of design to the values of the cost function. The mapping considered here includes the Euler equations for compressible flow discretized on unstructured meshes by a median-dual finite-volume scheme, the primal-to-dual mesh transformation, the mesh deformation, and the parameterization. The results of the present research concern the detailed derivations of expressions, equations, and algorithms that are necessary to calculate the gradient of the cost function. The discrete adjoint of the Euler equations and the exact dual-to-primal transformation of the gradient have been implemented for 2D and 3D applications in the code Edge, a program of Computational Fluid Dynamics used by Swedish industries. Moreover, techniques are proposed here in the aim to further reduce the computational cost of aerodynamic shape optimization. For instance, an interpolation scheme is derived based on Radial Basis Functions that can execute the deformation of unstructured meshes faster than methods based on an elliptic equation. In order to improve the accuracy of the shape, obtained by numerical optimization, a moving mesh adaptation scheme is realized based on a variable diffusivity equation of Winslow type. This adaptation has been successfully applied on a simple case of shape optimization involving a supersonic flow. An interpolation technique has been derived based on a mollifier in order to improve the convergence of the coupled mesh-flow equations entering the adaptive scheme. The method of adjoint derived here has also been applied successfully when coupling the Euler equations with the boundary-layer and parabolized stability equations, with the aim to delay the laminar-to-turbulent transition of the flow. The delay of transition is an efficient way to reduce the drag due to viscosity at high Reynolds numbers.

The objective of this work is to study the urban climate, mainly by focusing on urban temperature trends. The specific focus is to understand the reasons of increase in minimum temperature through observational and modelling techniques. For this purpose, the temperatures data from 1950 to 2004 measured on several meteorological stations of Pakistan is studied and analyzed. Daily averaged annual and seasonal minimum (Tmin) and maximum (Tmax) temperature data of 37 meteorological observatories of Pakistan (17 urban, 7 town and 13 rural) from 1950 to 2004 is first homogenized and then analyzed. The results show that after 1980s Tmin and Tmax increase faster than the period before 1980s at urban areas. During 1980-2004, the increase in Tmin at major urban stations is observed higher than the smaller towns and rural stations. To understand, the effect of the size of the city, changing land use and the building height on the evolution of minimum and maximum temperatures in urban areas has been studied by using the FVM (Finite Volume Model) model and the simulations are run for three days starting at 00:00 (GMT) on 19th day of each month and ending at 00:00 (GMT) on 22nd day of each month. For each month, 48 possible combinations of simulation scenarios are run (4*4*3) and in total, 576 simulations (48*12) are run for a year. The main results show that Tmin and Tmax increase when urban fraction u, city size r and building height h increase. But it is noticed that Tmax increases more than the Tmin when u increases, Tmin increases more than the Tmax when r increases and Tmin increases more than the Tmax when h increases. Among all urban factors (urban fraction u, city size r and building's height h), city size is the major factor that mainly contributes to increase the minimum temperature more than the maximum temperature in urban areas.

Lorsqu'une suspension concentrée est en écoulement, il est fréquent d'observer que la concentration en particules ne reste pas homogène mais que les particules migrent vers des régions préférentielles de l'écoulement. Globalement, il existe deux types de modèles pour décrire cette interaction entre l'écoulement et la structure qui apparaît dans la suspension. Les premiers sont assez phénoménologiques et reposent sur l'étude des collisions qui surviennent entre les particules en écoulement. Ils donnent lieu à une description de la migration en terme de diffusion des particules. Le second modèle, appelé "Suspension Balance Model" (SBM), fait appel à l'action des contraintes normales d'origine particulaire engendrées par l'écoulement. Ce modèle semble très pertinent mais son utilisation souffre du manque de données sur les contraintes normales dans les suspensions. Ce manuscrit rapporte une étude expérimentale et numérique de la rhéologie et de la migration induite par un écoulement dans des suspensions non-browniennes concentres. La partie expérimentale consiste à mesurer, en géométrie torsionnelle plan-plan, la viscosité, les deux différences de contraintes normales et le tenseur des contraintes particulaires. Les contraintes particulaires déterminées expérimentalement sont alors injectées dans le "Suspension Balance Model" qui relie le flux de particules à la divergence du tenseur des contraintes particulaires, dans le cas d'un écoulement de cisaillement simple. Les équations couplées de la conservation de la masse, des particules et du moment d'inertie sont implémentées dans OpenFOAM et résolues par la méthode des volumes finis. Les résultats numériques sont comparés à des résultats numériques et expérimentaux de la littérature. Enfin, le SBM est généralisé pour être utilisé dans tout type d'écoulement à 2 dimensions ; les cas du cisaillement d'un nuage de particules et de l'effet de la gravité dans un écoulement de Couette horizontal sont traités.

The aim of this research dissertation is at studying natural and mixed convections of fluid flows, and to develop and validate numerical schemes for interface tracking in order to treat incompressible and immiscible fluid flows, later. In a first step, an original numerical method, based on Finite Volume discretizations, is developed for modeling low Mach number flows with large temperature gaps. Three physical applications on air flowing through vertical heated parallel plates were investigated. We showed that the optimum spacing corresponding to the peak heat flux transferred from an array of isothermal parallel plates cooled by mixed convection is smaller than those for natural or forced convections when the pressure drop at the outlet keeps constant. We also proved that mixed convection flows resulting from an imposed flow rate may exhibit unexpected physical solutions; alternative model based on prescribed total pressure at inlet and fixed pressure at outlet sections gives more realistic results. For channels heated by heat flux on one wall only, surface radiation tends to suppress the onset of recirculations at the outlet and to unify the walls temperature. In a second step, the mathematical model coupling the incompressible Navier-Stokes equations and the Level-Set method for interface tracking is derived. Improvements in fluid volume conservation by using high order discretization (ENO-WENO) schemes for the transport equation and variants of the signed distance equation are discussed

The handling of gradient calculations on non-orthogonal meshes in the Finite Volume Method (FVM) is important in the modelling of complex geometries, since different implementation methods have an influence on the accuracy and the stability of the solution. The application in the current study is the numerical solution of heat conduction in a complex geometry. It finds relevance in many engineering applications such as the Micro-Channel Heat Exchanger (MCHE) that acts as a recuperator in a High Temperature Reactor (HTR) power generation cycle. A program based on the FVM was developed in Excel for the solution of the diffusion equation on a non-orthogonal mesh. A test case of heat conduction in a rectangular block, meshed with a tetrahedral mesh, was solved with the Excel code. The same test case was solved with OpenFOAM. The results of the two codes were compared. Small differences were found and their origins were traced to slightly different implementation methods. Knowledge of the differences in implementation between the two codes resulted in a better understanding of the aspects that influenced accuracy and stability. Computations on meshes with the presence of mesh skewness and non-orthogonal mesh lines at boundaries were performed and an accompanying decrease in accuracy was observed. The results showed that the standard FVM as implemented in the Excel code and in OpenFOAM will need advanced methods to compensate for mesh skewness and non-orthogonality found at boundaries. During the study, a deeper knowledge and understanding was gained of the challenge of obtaining accurate solutions of heat conduction on non-orthogonal meshes. This knowledge may lead to the overall improvement of the simulation of heat transfer models in general and for the MCHE specifically. / Thesis (MIng (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.