ON FINITE DIFFERENCE SCHEMES FOR THE 3-D WAVE EQUATION USING NON-CARTESIAN GRIDS

(Abstract to follow

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

Massiv parallele Simulation von Mehrphasen- und Mehrkomponentenströmungen unter Anwendung des Lattice Boltzmann Verfahrens

This thesis reflects the work mainly performed within the research project FIMOTUM focusing on the determination of transport properties and mechanisms in unsaturated media. The efficient simulation of single- and multiphase flows at the pore scale in highly resolved natural porous media is one of the major topics in this work. For this purpose a simulation kernel which is based on the lattice Boltzmann method (LBM) has been developed and extensively validated. The LBM presented utilizes the Multiple Relaxation Time (MRT) model and fluid/wall boundary conditions of second order accuracy. The model has also been extended to solve multiphase, advection/diffusion and thermal flow problems. Due to the application of an optimized collision model and corresponding boundary conditions, the covered parameter space and the stability of the method could be greatly enhanced. Hence, it was possible to perform simulations in complex geometries at a large scale (2E11+ DoF) which have been obtained with an unprecedented accuracy. A second target of this thesis was the design and implementation of a simulation kernel to perform massively parallel computations with high efficiency. In order to obtain accurate simulation results at reasonable computational effort, a novel grid generation procedure has been developed. The robust and flexible method is based on the decoupling of input geometry and the actual computational grid. It is therefore excellently suited for the grid generation based on natural porous media data sets obtained by CT- or X-ray methods. Aspects concerning the increasing difficulties in pre- and post-processing of large data sets are discussed. Furthermore, special issues in high performance computing environments are highlighted and a tool chain to visualize scientific data in photo-realistic representation is described.Die vorliegende Dissertation gibt im Wesentlichen die Arbeiten wieder, die im Rahmen des FIMOTUM Projektes durchgeführt worden sind, welches sich vornehmlich auf die Untersuchung von Transporteigenschaften in ungesättigten porösen Medien fokussierte. Hierfür wurde ein Software-Prototyp auf Basis der Gitter Boltzmann Methode (LBM) entwickelt und ausführlich validiert. Die vorgestellte LB-Methode basiert auf dem Multiple-Relaxation-Time (MRT) Modell und verwendet Fluid/Wand Randbedingungen mit einer Genauigkeit 2. Ordnung. Das beschriebene Modell wurde zudem für die Simulation von Mehrphasen-, Advektion/Diffusions- und Thermalen Problemen erweitert. Durch die Optimierung des Kollisionsmodells und der entsprechenden Randbedingungen konnte der nutzbare Parameterraum deutlich vergrößert werden, so dass Simulationen in komplexen Geometrien mit mehr als 2.0E+11 Freiheitsgraden möglich wurden. Ein zweites Ziel dieser Arbeit war die Implementierung eines effizienten und hochparallelen Software-Prototypen zur Simulation von fluiddynamischen Problemen. Um möglichst genaue Ergebnisse bei mäßigem Ressourceneinsatz zu erzielen, wurde ein neuartiger Gittergenerierungsprozess entwickelt. Dieses robuste und flexible Verfahren basiert auf der Entkopplung von Eingangsgeometrie und dem eigentlichen Rechengitter. Daher eignet sich dieser Gittergenerator hervorragend für die Erzeugung eines numerischen Gitters aus digitalen Datensätzen natürlicher poröser Medien, wie bspw. Tomographie-Scans. Desweiteren werden, neben allgemeinen Problemen des Hochleistungsrechnens, die zunehmenden Schwierigkeiten bei der Verarbeitung der ständig steigenden Datenmengen im Pre- und Postprocessing diskutiert. Weiterhin wird, unterstützend zur Ergebnisanalyse, eine Prozesskette für die Erzeugung von fotorealistischen Visualisierungen aus Simulationsdaten beschrieben

Lattice Boltzmann methods for direct numerical simulation of turbulent fluid flows

We study the use of lattice Boltzmann (LB) methods for simulation of turbulent fluid flows motivated by their high computational throughput and amenability to highly parallel platforms such as graphics processing units (GPUs). Several algorithmic improvements are unearthed including work on non-unit Courant numbers, the force operator, use of alternative topologies based on face and body centered cubic lattices and a new formulation using a generalized eigendecomposition that allows a new freedom in tuning the eigenvectors of the linearised collision operator. Applications include a variable bulk viscosity and the use of a stretched grid, our implementation of which reduces errors present in previous efforts. We present details for numerous lattices including all required matrices, their moments the procedures and programs used to generate these and perform linear stability analysis. Small Mach number flows where density variations are negligible except in the buoyancy force term allow the use of a highly accurate finite volume solver to simulate the evolution of the buoyancy field which is coupled to the LB simulation as an external force. We use a multidimensional flux limited third order flux integral based advection scheme. The simplified algorithm we have devised is easier to implement, has higher performance and does not sacrifice any accuracy compared to the leading alternative. Our algorithm is particularly suited to an outflow based implementation which furthers the stated benefits. We present numerical experiments confirming the third order accuracy of our scheme when applied to multidimensional advection. The coupled solver is implemented in a new code that runs in parallel across multiple machines using GPUs. Our code achieves high computational throughput and accuracy and is used to simulate a range of turbulent flows. Details regarding turbulent channel flow and sheared convective boundary layer simulations are presented including some new insight into the scaling properties of the latter flow

Image-based Modeling of Flow through Porous Media: Development of Multiscale Techniques for the Pore Level

Increasingly, imaging technology allows porous media problems to be modeled at microscopic and sub-microscopic levels with finer resolution. However, the physical domain size required to be representative of the media prohibits comprehensive micro-scale simulation. A hybrid or multiscale approach is necessary to overcome this challenge. In this work, a technique was developed for determining the characteristic scales of porous materials, and a multiscale modeling methodology was developed to better understand the interaction/dependence of phenomena occurring at different microscopic scales. The multiscale method couples microscopic simulations at the pore and sub-pore scales. Network modeling is a common pore-scale technique which employs severe assumptions, making it more computationally efficient than direct numerical simulation, enabling simulation over larger length scales. However, microscopic features of the medium are lost in the discretization of a material into a network of interconnected pores and throats. In contrast, detailed microstructure and flow patterns can be captured by modern meshing and direct numerical simulation techniques, but these models are computationally expensive. In this study, a data-driven multiscale technique has been developed that couples the two types of models, taking advantage of the benefits of each. Specifically, an image-based physically-representative pore network model is coupled to an FEM (finite element method) solver that operates on unstructured meshes capable of resolving details orders of magnitude smaller than the pore size. In addition to allowing simulation at multiple scales, the current implementation couples the models using a machine learning approach, where results from the FEM model are used to learn network model parameters. Examples of the model operating on real materials are given that demonstrate improvements in network modeling enabled by the multiscale framework. The framework enables more advanced multiscale and multiphysics modeling – an application to particle straining problems is shown. More realistic network filtration simulations are possible by incorporating information from the sub-pore-scale. New insights into the size exclusion mechanism of particulate filtration were gained in the process of generating data for machine learning of conductivity reduction due to particle trapping. Additional tests are required to validate the multiscale network filtration model, and compare with experimental findings in literature

Pattern Formation and Stability in Magnetic Colloids

This book presents a selection of works on pattern formation and stability of magnetic colloids. Magnetic liquids can be investigated in different scenarios. Geometry (quasi 1, 2 and 3 dimensional vessels ), scales (molecules, macroscopic particles) and the type of suspension (e.g., ferromagnetic, superparamagnetic) employed in experiments completely modify the aggregation process. The observed patterns in the fluid range from surface waves to bulk chains and bundles. The approaches presented in this book use standard statistical means such as the Gibbs free energy and chemical potential. Numerical works are implemented employing methods such as Monte Carlo or Langevin dynamics simulations. Kinetic theory is used in theoretical approaches being successfully applied to algorithms such as the Lattice-Boltzmann method