A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows

We compare the lattice Boltzmann equation (LBE) and the gas-kinetic scheme (GKS) applied to 2D incompressible laminar flows. Although both methods are derived from the Boltzmann equation thus share a common kinetic origin, numerically they are rather different. The LBE is a finite difference method, while the GKS is a finite-volume one. In addition, the LBE is valid for near incompressible flows with low-Mach number restriction Ma < 0.3, while the GKS is valid for fully compressible flows. In this study, we use the generalized lattice Boltzmann equation (GLBE) with multiple-relaxation-time (MRT) collision model, which overcomes all the apparent defects in the popular lattice BGK equation. We use both the LBE and GKS methods to simulate the flow past a square block symmetrically placed in a 2D channel with the Reynolds number Re between 10 and 300. The LBE and GKS results are validated against the well-resolved results obtained using finite-volume method. Our results show that both the LBE and GKS yield quantitatively similar results for laminar flow simulations, and agree well with existing ones, provided that sufficient grid resolution is given. For 2D problems, the LBE is about 10 and 3 times faster than the GKS for steady and unsteady flow calculations, respectively, while the GKS uses less memory. We also observe that the GKS method is much more robust and stable for under-resolved cases due to its upwinding nature and interpolations used in calculating fluxes. (C) 2008 Elsevier Inc. All rights reserved

Lattice Boltzmann modeling for shallow water equations using high performance computing

The aim of this dissertation project is to extend the standard Lattice Boltzmann method (LBM) for shallow water flows in order to deal with three dimensional flow fields. The shallow water and mass transport equations have wide applications in ocean, coastal, and hydraulic engineering, which can benefit from the advantages of the LBM. The LBM has recently become an attractive numerical method to solve various fluid dynamics phenomena; however, it has not been extensively applied to modeling shallow water flow and mass transport. Only a few works can be found on improving the LBM for mass transport in shallow water flows and even fewer on extending it to model three dimensional shallow water flow fields. The application of the LBM to modeling the shallow water and mass transport equations has been limited because it is not clearly understood how the LBM solves the shallow water and mass transport equations. The project first focuses on studying the importance of choosing enhanced collision operators such as the multiple-relaxation-time (MRT) and two-relaxation-time (TRT) over the standard single-relaxation-time (SRT) in LBM. A (MRT) collision operator is chosen for the shallow water equations, while a (TRT) method is used for the advection-dispersion equation. Furthermore, two speed-of-sound techniques are introduced to account for heterogeneous and anisotropic dispersion coefficients. By selecting appropriate equilibrium distribution functions, the standard LBM is extended to solve three-dimensional wind-driven and density-driven circulation by introducing a multi-layer LB model. A MRT-LBM model is used to solve for each layer coupled by the vertical viscosity forcing term. To increase solution stability, an implicit step is suggested to obtain stratified flow velocities. Numerical examples are presented to verify the multi-layer LB model against analytical solutions. The model’s capability of calculating lateral and vertical distributions of the horizontal velocities is demonstrated for wind- and density- driven circulation over non-uniform bathymetry. The parallel performance of the LBM on central processing unit (CPU) based and graphics processing unit (GPU) based high performance computing (HPC) architectures is investigated showing attractive performance in relation to speedup and scalability

Numerical Simulations of Thermal Systems-Applications To Fuel Chemistry, Nanofluid Heat Transfer And Aerosol Particle Transport.

In this dissertation, three topics in thermal systems are investigated: 1) the effect of methyl-ester content on combustion chemistry of a biodiesel surrogate; 2) the effects of non-uniform particle sizes and fluid temperature on heat transfer characteristics of liquid water containing alumina nano-particles; 3) the effects of obstacle arrangements on transport of aerosol particles in channel flows. The investigation focuses on computational modeling and analysis in the above problems. In the first study, a kinetic modeling comparison of methyl butanoate and n-butane, its corresponding alkane, contrasts the combustion of methyl esters and normal alkanes, with the aim of understanding the effect of the methyl ester moiety. A fuel-breakdown model [J. Org. Chem. 2008, 73, 94; J. Phys. Chem. A 2008, 112, 51] is added to existing chemical kinetic mechanisms to improve the prediction of CO2 formation from MB decomposition. Sensitivity and reaction pathway analysis show that the absence of negative temperature coefficient behaviors and reduction of soot precursors can be ascribed to the effect of the methyl ester. The second study analyzes the heat transfer and fluid flow of natural convection in a cavity filled with Al2O3/water nanofluid that operates within differentially heated walls. The Navier-Stokes and energy equations are solved numerically, coupling the model of effective thermal conductivity [J. Phys. D 2006, 39, 4486] and model of effective dynamic viscosity [Appl. Phys. Lett. 2007, 91, 243112]. The numerical simulations explore the range where the heat transfer uncertainties can be affected by the operating conditions of the nanoparticles. Furthermore, the suppressed heat transfer phenomena are in good agreement with the latest experimental data of Ho et al. [Int. J. Therm. Sci. 2010, 49, 1345]. Finally, by using a simple lattice Boltzmann model coupled with a Lagrangian formalism, this study investigates the dispersion and deposition of aerosol particles over staggered obstacles in a two-dimensional channel flow. Particle motion mechanisms considered in the particle phase equation include drag, gravity, lift and Brownian forces. In this study, the results highlight the range of particle dimensions where the particle deposition can be affected by the arrangement of blocks placed in the channel flow.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86287/1/kclin_1.pd

Compressible Shear Flow Transition and Turbulence: Enhancement of GKM Numerical Scheme and Simulation/Analysis of Pressure Effects on Flow Stabilization

Despite significant advancements in the understanding of fluid flows, combustion and material technologies, hypersonic flight still presents numerous technological challenges. In hypersonic vehicles turbulence is critical in controlling heat generation in the boundary layer, mixing inside the combustor, generation of acoustic noise, and mass flow in the intake. The study of turbulence in highly compressible flows is challenging compared to incompressible due to a drastic change in the behavior of pressure and a relaxation of the incompressibility constraint. In addition fluid flow inside a flight vehicle is complicated by wall-effects, heat generation and complex boundary conditions. Homogeneous shear flow contains most of the relevant physics of boundary and mixing layers without the aforementioned complicating effects. In this work we aim to understand and characterize the role of pressure, velocity-pressure interaction, velocity-thermodynamics interaction in the late-stage transition-to-turbulence regime in a high speed shear dominated flow by studying the evolution of perturbations in in a high Mach number homogeneous shear flow. We use a modal-analysis based approach towards understanding the statistical behavior of turbulence. Individual Fourier waves constituting the initial flow field are studied in isolation and in combination to understand collective statistical behavior. We demonstrate proof of concept of novel acoustic based strategies for controlling the onset of turbulence. Towards this goal we perform direct numerical simulations (DNS) in three studies: (a) development and evaluation of gas kinetic based numerical tool for DNS of compressible turbulence, and perform detailed evaluation of the efficacy of different interpolation schemes in capturing solenoidal and dilatational quantities, (b) modal investigation in the behavior of pressure and isolation of linear, non-linear, inertial and pressure actions, and (c) modal investigation in the possible acoustic based control strategies in homogeneously sheared compressible flows. The findings help to understand the manifestation of the effects of compressibility on transition and turbulence via the velocity-pressure interactions and the action of individual waves. The present study helps towards the design of control mechanisms for compressible turbulence and the development of physically consistent pressure strain correlation models

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

DEVELOPMENT OF GAS KINETIC FLUX SOLVERS AND THEIR APPLICATIONS

Ph.DDOCTOR OF PHILOSOPH