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The field of Computational Fluid Dynamics (CFD) is in a continual state of advancement due to new numerical techniques, optimization of existing codes, and the increase in memory and processing speeds of computers. In this thesis, the solution technique for a pre-existing Navier-Stokes flow solver is adapted from an explicit Runge Kutta method to a Lower-Upper Symmetric Gauss-Seidel (LU-SGS) implicit time integration method. Explicit time integration methods were originally used in CFD codes because these methods require less memory. Information needed to advance the flow in time is localized to each grid point. These explicit methods are, however, restricted by time step sizes due to stability criteria. In contrast, implicit methods are unaffected by a large time step sizes but are restricted by memory requirements due to the complexities of unstructured grids. The implementation of LU-SGS performs grid re-ordering for unstructured meshes because of the coupling of grid points in the integration method's solution. The explicit and implicit flow solvers were tested for inviscid flows in incompressible, compressible, and transoinc flow regimes. The results found by comparing the implicit and explicit algorithms revealed a significant speed up in convergence to steady state by the LU-SGS method in terms of iteration number and CPU time per iteration.

In der Version 2.0 des Simulationskopplungsstandards FMI (Functional Mockup Interface) wird die Möglichkeit zur Speicherung und Wiederherstellung einer Simulationseinheit/FMU (Functional Mockup Unit) definiert. Dieses ist eine elementare Voraussetzung für iterierende Co-Simulations-Masteralgorithmen, wie z.B. Gauss-Seidel oder Newton-Iteration. Für die gekoppelte Simulation von solchen Simulationseinheiten ist ein Co-Simulations-Master erforderlich. Das Simulationsmasterprogramm MASTERSIM ist ein solcher Co-Simulations-Master und enthält zahlreiche Algorithmen und eine effiziente Verwaltung von Simulationseinheiten unter Verwendung dieser neuen Schnittstellenfunktionen. Dieser Artikel dokumentiert grundlegende Co-Simulations-Algorithmen und beteiligte Parameter und illustriert deren Einfluss anhand eines Testbeispiels.:1. Grundlagen 2. Zeitintegration 3. Simulationsperformance 4. Testbeispiel 5. Kopplungsalgorithmen 6. Zusammenfassung

Cette thèse présente quelques propriétés des sous-variétés lagrangiennes monotones. On résoud d'abord une conjecture de Barraud et Cornea dans le cadre monotone en montrant que le rayon de Gromov relatif à deux lagrangiennes dans la même classe d'isotopie hamiltonienne donne une borne inférieure à la distance de Hofer entre ces deux mêmes lagrangiennes. Le cas non-monotone de cette conjecture reste ouvert encore. On définit toutes les structures nécessaires à l'énoncé et à la preuve de cette conjecture. Deuxièmement, on définit une nouvelle version d'un morphisme de Seidel relatif à l'aide des cobordismes lagrangiens de Biran et Cornea. On montre que cette version est chaîne-homotope aux différentes autres versions apparaissant dans la littérature. Que toutes ces définitions sont équivalentes fait partie du folklore mais n'apparaît pas dans la littérature. On conclut par une conjecture qui identifie un triangle exact obtenu par chirurgie lagrangienne et un autre dû à Seidel et faisant intervenir le twist de Dehn symplectique. / We present in this thesis a few properties of monotone Lagrangian submanifolds. We first solve a conjecture of Barraud and Cornea in the monotone setting by showing that the relative Gromov radius of two Hamiltonian-isotopic Lagrangians gives a lower bound on the Hofer distance between them. The general non-monotone case remains open to this day. We define all the structures relevant to state and prove the conjecture. We then define a new version of a Lagrangian Seidel morphism through the recently introduced Lagrangian cobordisms of Biran and Cornea. We show that this new version is chain-homotopic to various other versions appearing in the litterature. That all these previous versions are the same is folklore but did not appear in the litterature. We conclude with a conjecture claiming that an exact triangle obtained by Lagrangian surgery is isomorphic to an exact triangle of Seidel involving the symplectic Dehn twist.

Cette thèse présente quelques propriétés des sous-variétés lagrangiennes monotones. On résoud d'abord une conjecture de Barraud et Cornea dans le cadre monotone en montrant que le rayon de Gromov relatif à deux lagrangiennes dans la même classe d'isotopie hamiltonienne donne une borne inférieure à la distance de Hofer entre ces deux mêmes lagrangiennes. Le cas non-monotone de cette conjecture reste ouvert encore. On définit toutes les structures nécessaires à l'énoncé et à la preuve de cette conjecture. Deuxièmement, on définit une nouvelle version d'un morphisme de Seidel relatif à l'aide des cobordismes lagrangiens de Biran et Cornea. On montre que cette version est chaîne-homotope aux différentes autres versions apparaissant dans la littérature. Que toutes ces définitions sont équivalentes fait partie du folklore mais n'apparaît pas dans la littérature. On conclut par une conjecture qui identifie un triangle exact obtenu par chirurgie lagrangienne et un autre dû à Seidel et faisant intervenir le twist de Dehn symplectique. / We present in this thesis a few properties of monotone Lagrangian submanifolds. We first solve a conjecture of Barraud and Cornea in the monotone setting by showing that the relative Gromov radius of two Hamiltonian-isotopic Lagrangians gives a lower bound on the Hofer distance between them. The general non-monotone case remains open to this day. We define all the structures relevant to state and prove the conjecture. We then define a new version of a Lagrangian Seidel morphism through the recently introduced Lagrangian cobordisms of Biran and Cornea. We show that this new version is chain-homotopic to various other versions appearing in the litterature. That all these previous versions are the same is folklore but did not appear in the litterature. We conclude with a conjecture claiming that an exact triangle obtained by Lagrangian surgery is isomorphic to an exact triangle of Seidel involving the symplectic Dehn twist.

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No description available.

Nuclear reactor design requires the calculation of integral core parameters and power and radiation profiles. These physical parameters are obtained by the solution of the linear neutron transport equation over the geometry of the reactor. In order to represent the fine structure of the nuclear core a very small geometrical mesh size should be used, but the computational capacity available these days is still not enough to solve these transport problems in the time range (hours-days) that would make the method useful as a design tool. This problem is traditionally solved by the solution of simple, smaller problems in specific parts of the core and then use a procedure known as homogenization to create average material properties and solve the full problem with a wider mesh size. The iterative multi-level solution procedure is inspired in this multi-stage approach, solving the problem at fuel-pin (cell) level, fuel assembly and nodal levels. The nested geometrical structure of the finite element representation of a reactor can be used to create a set of restriction/prolongation operators to connect the solution in the different levels. The procedure is to iterate between the levels, solving for the error in the coarse level using as source the restricted residual of the solution in the finer level. This way, the complete problem is only solved in the coarsest level and in the other levels only a pair of restriction/interpolation operations and a relaxation is required. In this work, a multigrid solver is developed for the in-moment equation of the spherical harmonics, finite element formulation of the second order transport equation. This solver is implemented as a subroutine in the code EVENT. Numerical tests are provided as a standalone diffusion solver and as part of a block Jacobi transport solver.

Modeling and simulation of granular matter has important applications in both natural science and industry. One widely used method is the discrete element method (DEM). It can be used for simulating granular matter in the gaseous, liquid as well as solid regime whereas alternative methods are in general applicable to only one. Discrete element analysis of large systems is, however, limited by long computational time. A number of solutions to radically improve the computational efficiency of DEM simulations are developed and analysed. These include treating the material as a nonsmooth dynamical system and methods for reducing the computational effort for solving the complementarity problem that arise from implicit treatment of the contact laws. This allow for large time-step integration and ultimately more and faster simulation studies or analysis of more complex systems. Acceleration methods that can reduce the computational complexity and degrees of freedom have been invented. These solutions are investigated in numerical experiments, validated using experimental data and applied for design exploration of iron ore pelletising systems. / <p>This work has been generously supported by Algoryx Simulation, LKAB (dnr 223-</p><p>2442-09), Umeå University and VINNOVA (2014-01901).</p>

Der Autor Rainer Gilles beschäftigt sich seit fast 30 Jahren intensiv mit der bekannten Firma aus der Elbmetropole. Es fiel ihm nicht leicht, der Firmengeschichte oder gar ihrem Begründer Bruno Naumann auf knappem Raum gerecht zu werden. Aus einer unglaublichen Fülle von Abbildungen, Plakaten und Objekten stellte die Redaktion ein paar Bildseiten zusammen, um den Leserinnen und Lesern einen Überblick über das Wirken dieser renommierten Fahrrad- und Nähmaschinenfabrik zu geben.