A non-hybrid method for the PDF equations of turbulent flows on unstructured grids

In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A set of parallel algorithms is proposed to provide an efficient solution of the PDF transport equation, modeling the joint PDF of turbulent velocity, frequency and concentration of a passive scalar in geometrically complex configurations. An unstructured Eulerian grid is employed to extract Eulerian statistics, to solve for quantities represented at fixed locations of the domain (e.g. the mean pressure) and to track particles. All three aspects regarding the grid make use of the finite element method (FEM) employing the simplest linear FEM shape functions. To model the small-scale mixing of the transported scalar, the interaction by exchange with the conditional mean model is adopted. An adaptive algorithm that computes the velocity-conditioned scalar mean is proposed that homogenizes the statistical error over the sample space with no assumption on the shape of the underlying velocity PDF. Compared to other hybrid particle-in-cell approaches for the PDF equations, the current methodology is consistent without the need for consistency conditions. The algorithm is tested by computing the dispersion of passive scalars released from concentrated sources in two different turbulent flows: the fully developed turbulent channel flow and a street canyon (or cavity) flow. Algorithmic details on estimating conditional and unconditional statistics, particle tracking and particle-number control are presented in detail. Relevant aspects of performance and parallelism on cache-based shared memory machines are discussed.Comment: Accepted in Journal of Computational Physics, Feb. 20, 200

State of the Art in the Optimisation of Wind Turbine Performance Using CFD

Wind energy has received increasing attention in recent years due to its sustainability and geographically wide availability. The efficiency of wind energy utilisation highly depends on the performance of wind turbines, which convert the kinetic energy in wind into electrical energy. In order to optimise wind turbine performance and reduce the cost of next-generation wind turbines, it is crucial to have a view of the state of the art in the key aspects on the performance optimisation of wind turbines using Computational Fluid Dynamics (CFD), which has attracted enormous interest in the development of next-generation wind turbines in recent years. This paper presents a comprehensive review of the state-of-the-art progress on optimisation of wind turbine performance using CFD, reviewing the objective functions to judge the performance of wind turbine, CFD approaches applied in the simulation of wind turbines and optimisation algorithms for wind turbine performance. This paper has been written for both researchers new to this research area by summarising underlying theory whilst presenting a comprehensive review on the up-to-date studies, and experts in the field of study by collecting a comprehensive list of related references where the details of computational methods that have been employed lately can be obtained

Approximation Algorithms for Geometric Networks

The main contribution of this thesis is approximation algorithms for several computational geometry problems. The underlying structure for most of the problems studied is a geometric network. A geometric network is, in its abstract form, a set of vertices, pairwise connected with an edge, such that the weight of this connecting edge is the Euclidean distance between the pair of points connected. Such a network may be used to represent a multitude of real-life structures, such as, for example, a set of cities connected with roads. Considering the case that a specific network is given, we study three separate problems. In the first problem we consider the case of interconnected `islands' of well-connected networks, in which shortest paths are computed. In the second problem the input network is a triangulation. We efficiently simplify this triangulation using edge contractions. Finally, we consider individual movement trajectories representing, for example, wild animals where we compute leadership individuals. Next, we consider the case that only a set of vertices is given, and the aim is to actually construct a network. We consider two such problems. In the first one we compute a partition of the vertices into several subsets where, considering the minimum spanning tree (MST) for each subset, we aim to minimize the largest MST. The other problem is to construct a $t$-spanner of low weight fast and simple. We do this by first extending the so-called gap theorem. In addition to the above geometric network problems we also study a problem where we aim to place a set of different sized rectangles, such that the area of their corresponding bounding box is minimized, and such that a grid may be placed over the rectangles. The grid should not intersect any rectangle, and each cell of the grid should contain at most one rectangle. All studied problems are such that they do not easily allow computation of optimal solutions in a feasible time. Instead we consider approximation algorithms, where near-optimal solutions are produced in polynomial time. In addition to the above geometric network problems we also study a problem where we aim to place a set of different sized rectangles, such that the area of their corresponding bounding box is minimized, and such that a grid may be placed over the rectangles. The grid should not intersect any rectangle, and each cell of the grid should contain at most one rectangle. All studied problems are such that they do not easily allow computation of optimal solutions in a feasible time. Instead we consider approximation algorithms, where near-optimal solutions are produced in polynomial time