No description available.

High-order numerical methods have been considered and implemented in order to assess their applicability in a range of complex ows centering on shockinduced turbulent mixing. Speci cally, Weighted Essentially Non-Oscillatory (WENO) variable reconstruction schemes of fth and ninth order accuracy have been investigated within the context of a nite volume Godunov solver. In addition to this there have been further numerical developments to assess the HLLC Riemann solver and various quasi-conservative multi-component models in conjunction with the high-order methods. Understanding the physics of fundamental ow instabilities and turbulence is increasingly necessary to the development of a vast range of engineering applications with relation to uid dynamics. It is desirable to develop numerical methods that possess su cient accuracy to capture the detail of such ows while remaining robust and viable in terms of cost. The WENO schemes have been tested on a number of cases in comparison with more traditional second-order MUSCL schemes. These include two and three dimensional, single and multi mode Richtmyer-Meshkov instabilities with differing initial perturbations, a cube of homogeneous decaying turbulence and two hypersonic geometry cases were simulated. The results from this research were consistent. The higher-order methods provided measurably greater resolution of small scale uctuations. By conducting grid convergence studies it was seen that the e ect of the higher-order methods was comparable to the e ect of increasing the number of grid points. The cost analysis repeatedly showed that despite the additional cost of using a higher-order method they were much better value as they could resolve ow features on a signi cantly coarser grid. The high-order methods were not only validated for a range of ow problems but shown to o er great value for their additional cost; they could potentially help advance understanding and development in a wide range of elds much faster than is currently the case.

This thesis presents the construction, the analysis and the verification of a new form of higher than second order fluctuation splitting discretisation for the solution of steady conservation laws on unstructured meshes. This is an alternative approach to the two existing higher than second order fluctuation splitting schemes, which use submesh reconstruction (developed by Abgrall and Roe) and gradient recovery (developed by Caraemi) to obtain the loacl higher degree polynomials used to evaluate the fluctuation. The new higher than second order approach constructs the polynomial interpolant of the values of the dependent variables at an appropriate number of carefully chosen mesh nodes. As they stand, none of the higher than second order methods can guarantee the absence of spurious oscillations from the flow without the application of an additional smoothing stage. The implementation of a technique that removes unphysical oscillations (devised by Hubbard) as part of a new higher than second order approach will be outlined. The design steps and theoretical bases are discussed in depth. The new higher than second order approach is examined and analysed through application to a series of linear and nonlinear scalar problems, using a pseudo-time-stepping technique to reach steady state solution on two-dimensional structured and unstructured meshes. The results demonstrate its effectiveness in approximating the linear and nolinear scalar problems. This thesis also addresses the development and examination of a multistage high order (in space and time) fluctuation splitting scheme for two-dimensional unsteady scalar advection on triangular unstructured meshes. the method is similar in philosophy to that of multistep high order (in space and time) fluctuation splitting scheme for the approximation of time-dependent hyperbolic conservation laws. The construction and implementation of the high order multistage time-dependent method are discussed in detail and its performance is illustrated using several standard test problems. The multistage high order time-dependent method is evaluated in the context of existing fluctuation splitting approaches to modelling time-dependent problems and some suggestions for their future development are made. Results presented indicate that the multistage high orer method can produce a slightly more accurate solution than the multistep high order method.

Includes summary / Bibliography: leaves 108-112 / vii, 112 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1989

We present a unifying framework for the global optimization of functions which are expensive to evaluate. The framework is based on a Bayesian interpretation of radial basis function interpolation which incorporates existing methods such as Kriging, Gaussian process regression and neural networks. This viewpoint enables the application of Bayesian decision theory to derive a sequential global optimization algorithm which can be extended to include existing algorithms of this type in the literature. By posing the optimization problem as a sequence of sampling decisions, we optimize a general cost function at each stage of the algorithm. An extension to multi-stage decision processes is also discussed. The key idea of the framework is to replace the underlying expensive function by a cheap surrogate approximation. This enables the use of existing branch and bound techniques to globally optimize the cost function. We present a rigorous analysis of the canonical branch and bound algorithm in this setting as well as newly developed algorithms for other domains including convex sets. In particular, by making use of Lipschitz continuity of the surrogate approximation, we develop an entirely new algorithm based on overlapping balls. An application of the framework to the integration of expensive functions over rectangular domains and spherical surfaces in low dimensions is also considered. To assess performance of the framework, we apply it to canonical examples from the literature as well as an industrial model problem from oil reservoir simulation.

L’étude engagée dans cette thèse consiste à mettre en place une modélisation numérique fiable et complète du transport et du dépôt des particules dans un écoulement pulmonaire en se basant sur l’utilisation du code de calcul commercial CFD-ACE. Ce code intègre un solveur fluide qui résout les équations de Navier-Stokes incompressibles dans une formulation volumes finis. Le logiciel CFD-GEOM a été utilisé pour créer les surfaces en 3D de la géométrie générique du modèle de Weibel et ainsi générer le maillage non-structuré tétraèdrique en volumes finis. Dans le cadre de ce travail, il est supposé que le flux d’air est laminaire, stationnaire (ou instationnaire uniquement dans les modèles bronchiques) et incompressible ; les particules de diamètre 5μm sont sphériques et sans interaction. Le pourcentage global et local du dépôt des particules dans les poumons peut s’exprimer comme une efficacité de dépôt et se définit par le rapport entre le nombre de particules déposées dans une région donnée et le nombre total de particules admises initialement à l’entrée de la conduite. L’efficacité de dépôt dépend fortement du nombre de Stokes d’entrée, des conditions d’admission en termes de profil de vitesse du fluide (nombre de Reynolds d’entrée), de la distribution et des caractéristiques des particules. Nous avons donc modélisé avec succès les écoulements ainsi que le transport et le dépôt de particules dans des configurations simples (modèles de Weibel) et des configurations réalistes (poumons de rat et du lapin) et ce que l’on en peut dire c’est que la simulation, bien que coûteuse (surtout pour le dépôt des particules), ne présente pas de difficultés insurmontables. Par contre l’obtention d’une géométrie réaliste et la génération du maillage associé reste une étape délicate. / The study undertaken in this thesis is to develop a reliable and comprehensive numerical modeling of transport and deposition of particles in pulmonary flow based on the use of CFDACE computer code. This code includes a fluid solver that solves the Navier-Stokes in a finite volume formulation. The CFD-GEOM software was used to create 3D surfaces of the geometry of the generic model of Weibel and generate the unstructured tetrahedral finite volume mesh. As part of this work, it is assumed that the airflow is laminar, steady (unsteady only in bronchial models) ; the particles of diameter 5μm are spherical and noninteracting. The percentage of global and local particle deposition in the lungs can be expressed as a deposition efficiency and is defined as the ratio between the number of particles deposited in a given area and the total number of particles initially admitted to the entrance of lungs. The deposition efficiency depends strongly on the Stokes number of entry, the airflow fluid velocity profile (Reynolds number at the inlet), the distribution and characteristics of particles. We have successfully modeled the flow, the transport and deposition of particles in simple configurations (models of Weibel), realistic configurations (lungs of rats and rabbits) and we can conclude that the simulation, al though expensive in terms of computer memory & time (especially for particle deposition), does not present insurmountable difficulties. On the other hand, obtaining a realistic geometry and mesh generation main a challenge.

Cette thèse propose différentes méthodes numériques pour simuler les plasmas ou les faisceaux de particules chargées à coût réduit. Le mouvement de particules chargées soumises à un champ électromagnétique est régi par l'équation de Vlasov, couplée aux équations de Maxwell ou de Poisson. Dans la première partie, une méthode multi-fluides est utilisée pour la résolution du système de Vlasov-Poisson 1D. Elle est basée sur la connaissance a priori de la forme prise par la fonction de distribution f. Ce type de méthodes est plutôt adapté aux systèmes restant proches de l'état d'équilibre. La deuxième partie propose de décomposer f en une partie d'équilibre et une perturbation. L'équilibre est résolu par une méthode fluide, la perturbation par une méthode cinétique plus précise. On construit un schéma préservant l'asymptotique pour le système de Vlasov-Poisson-BGK basé sur une telle décomposition. On étudie dans la troisième partie la méthode PIC en géométrie 2D axisymétrique. Un travail basé sur l'analyse isogéométrique est présenté ainsi qu'un code PIC - Galerkin Discontinu parallélisé sur carte graphique. / This thesis presents different numerical methods for the simulation of plasmas or charged particles beams with reduced cost. Movement of charged particles in an electromagnetic field is given by the Vlasov equation, coupled to the Maxwell equations for the electromagnetic field, or to the Poisson equation. In the first part, a multi-fluid method is used for solving the 1D Vlasov-Poisson system. It is based on the a priori knowledge of the shape of f. This kind of methods is rather adapted to systems staying close to the equilibrium. The second part presents the decomposition of f between an equilibrium part and a perturbation. The equilibrium part is solved by a fluid method whereas we use a kinetic method for the perturbation. We construct an asymptotic preserving scheme for the Vlasov-Poisson-BGK system using such a decomposition. The third part deals with the PIC method in 2D axisymmetric geometry. A work based on isogeometric analysis is presented, and then a PIC - Discontinuous Galerkin program computed on graphic card.