Development and Monte Carlo validation of a finite element reactor analysis framework

This study presents the development and Monte Carlo validation of a continuous Galerkin finite element reactor analysis framework. In its current state, the framework acts as an interface between the mesh preparation software GMSH and the sparse linear solvers in MATLAB, for the discretization and approximation of 1-D, 2-D, and 3-D linear partial differential equations. Validity of the framework is assessed from the following two benchmarking activities: the 2-D IAEA PWR benchmark; and the 2-D Missouri Science and Technology Reactor benchmark proposed within this study. The 2-D IAEA PWR multi-group diffusion benchmark is conducted with the following discretization schemes: linear, quadratic, and cubic triangular elements; linear and quadratic rectangular elements of mesh sizes 10, 5, 2, 1, 0.5 cm. Convergence to the reference criticality eigenvalue of 1.02985 is observed for all cases. The proposed 2-D MSTR benchmark is prepared through translation of an experimentally validated 120w core configuration MCNP model into Serpent 2. Validation of the Serpent 2 model is attained from the comparison of criticality eigenvalues, flux traverses, and two 70-group energy spectrums within fuel elements D5 and D9. Then, a two-group 2-D MSTR benchmark of the 120w core configuration is prepared with the spatial homogenization methodology implemented within Serpent 2. Final validation of the framework is assessed from the comparison of criticality eigenvalues and spatial flux solutions of the diffusion and simplified spherical harmonics SP3 models. The diffusion model resulted in a difference in reactivity of Δρ =-1673.93 pcm and the SP3 model resulted in a difference of Δρ = -777.60 pcm with respect to the Serpent 2 criticality eigenvalues --Abstract, page iii

Application of general semi-infinite Programming to Lapidary Cutting Problems

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented

Ein Gas-Kinetic Scheme Ansatz zur Modellierung und Simulation von Feuer auf massiv paralleler Hardware

This work presents a simulation approach based on a Gas Kinetic Scheme (GKS) for the simulation of fire that is implemented on massively parallel hardware in terms of Graphics Processing Units (GPU) in the framework of General Purpose computing on Graphics Processing Units (GPGPU). Gas kinetic schemes belong to the class of kinetic methods because their governing equation is the mesoscopic Boltzmann equation, rather than the macroscopic Navier-Stokes equations. Formally, kinetic methods have the advantage of a linear advection term which simplifies discretization. GKS inherently contains the full energy equation which is required for compressible flows. GKS provides a flux formulation derived from kinetic theory and is usually implemented as a finite volume method on cell-centered grids. In this work, we consider an implementation on nested Cartesian grids. To that end, a coupling algorithm for uniform grids with varying resolution was developed and is presented in this work. The limitation to local uniform Cartesian grids allows an efficient implementation on GPUs, which belong to the class of many core processors, i.e. massively parallel hardware. Multi-GPU support is also implemented and efficiency is enhanced by communication hiding. The fluid solver is validated for several two- and three-dimensional test cases including natural convection, turbulent natural convection and turbulent decay. It is subsequently applied to a study of boundary layer stability of natural convection in a cavity with differentially heated walls and large temperature differences. The fluid solver is further augmented by a simple combustion model for non-premixed flames. It is validated by comparison to experimental data for two different fire plumes. The results are further compared to the industry standard for fire simulation, i.e. the Fire Dynamics Simulator (FDS). While the accuracy of GKS appears slightly reduced as compared to FDS, a substantial speedup in terms of time to solution is found. Finally, GKS is applied to the simulation of a compartment fire. This work shows that the GKS has a large potential for efficient high performance fire simulations.Diese Arbeit präsentiert einen Simulationsansatz basierend auf einer gaskinetischen Methode (eng. Gas Kinetic Scheme, GKS) zur Simulation von Bränden, welcher für massiv parallel Hardware im Sinne von Grafikprozessoren (eng. Graphics Processing Units, GPUs) implementiert wurde. GKS gehört zur Klasse der kinetischen Methoden, die nicht die makroskopischen Navier-Stokes Gleichungen, sondern die mesoskopische Boltzmann Gleichung lösen. Formal haben kinetische Methoden den Vorteil, dass der Advektionsterms linear ist. Dies vereinfacht die Diskretisierung. In GKS ist die vollständige Energiegleichung, die zur Lösung kompressibler Strömungen benötigt wird, enthalten. GKS formuliert den Fluss von Erhaltungsgrößen basierend auf der gaskinetischen Theorie und wird meistens im Rahmen der Finiten Volumen Methode umgesetzt. In dieser Arbeit betrachten wir eine Implementierung auf gleichmäßigen Kartesischen Gittern. Dazu wurde ein Kopplungsalgorithmus für die Kombination von Gittern unterschiedlicher Auflösung entwickelt. Die Einschränkung auf lokal gleichmäßige Gitter erlaubt eine effiziente Implementierung auf GPUs, welche zur Klasse der massiv parallelen Hardware gehören. Des Weiteren umfasst die Implementierung eine Unterstützung für Multi-GPU mit versteckter Kommunikation. Der Strömungslöser ist für zwei und dreidimensionale Testfälle validiert. Dabei reichen die Tests von natürlicher Konvektion über turbulente Konvektion bis hin zu turbulentem Zerfall. Anschließend wird der Löser genutzt um die Grenzschichtstabilität in natürlicher Konvektion bei großen Temperaturunterschieden zu untersuchen. Darüber hinaus umfasst der Löser ein einfaches Verbrennungsmodell für Diffusionsflammen. Dieses wird durch Vergleich mit experimentellen Feuern validiert. Außerdem werden die Ergebnisse mit dem gängigen Brandsimulationsprogramm FDS (eng. Fire Dynamics Simulator) verglichen. Die Qualität der Ergebnisse ist dabei vergleichbar, allerdings ist der in dieser Arbeit entwickelte Löser deutlich schneller. Anschließend wird das GKS noch für die Simulation eines Raumbrandes angewendet. Diese Arbeit zeigt, dass GKS ein großes Potential für die Hochleistungssimulation von Feuer hat

Interface-Resolving Simulations of Gas-Liquid Two-Phase Flows in Solid Structures of Different Wettability

This PhD study is devoted to numerical investigations of two-phase flows on and through elementary and complex solid structures of varying wettability. The phase-field method is developed and implemented in OpenFOAM®. The numerical method/code is verified by a series of test cases of two-phase flows, and then applied to investigate: (1) droplet wetting on solid surfaces; (2) air bubble rising and interacting with cellular structures and (3) gas-liquid interfacial flows in foam structures