Inertial Frame Independent Forcing for Discrete Velocity Boltzmann Equation: Implications for Filtered Turbulence Simulation

We present a systematic derivation of a model based on the central moment lattice Boltzmann equation that rigorously maintains Galilean invariance of forces to simulate inertial frame independent flow fields. In this regard, the central moments, i.e. moments shifted by the local fluid velocity, of the discrete source terms of the lattice Boltzmann equation are obtained by matching those of the continuous full Boltzmann equation of various orders. This results in an exact hierarchical identity between the central moments of the source terms of a given order and the components of the central moments of the distribution functions and sources of lower orders. The corresponding source terms in velocity space are then obtained from an exact inverse transformation due to a suitable choice of orthogonal basis for moments. Furthermore, such a central moment based kinetic model is further extended by incorporating reduced compressibility effects to represent incompressible flow. Moreover, the description and simulation of fluid turbulence for full or any subset of scales or their averaged behavior should remain independent of any inertial frame of reference. Thus, based on the above formulation, a new approach in lattice Boltzmann framework to incorporate turbulence models for simulation of Galilean invariant statistical averaged or filtered turbulent fluid motion is discussed.Comment: 37 pages, 1 figur

Entwicklung und Validierung von Turbulenzmodellen für Lattice Boltzmann Methoden

Computational fluid mechanics has become a standard approach in many branches of engineering. Simulation of flow on the building- and infrastructure scale, however, remains very challenging and is mostly restricted to basic research at the present stage. In particular, accurate, three-dimensional, time-resolved simulation such as Large Eddy Simulation is still rarely used despite its potential. On the other hand, it is reasonable to expect a growing influence of these methods as computers become more powerful and numerical methods evolve. In the present work the Lattice Boltzmann method is chosen as a starting point to analyze simulations of flow around buildings. This approach appears to be particularly apt for such applications due to its very good scalability with respect to parallel computing. Different variants of the Lattice Boltzmann method, namely the Lattice Bhatnagar-Gross-Krook method, the Multiple Relaxation Time method, and variants of the Cascaded Lattice Boltzmann (CLB) method have been implemented and compared on the basis of standard benchmarks. Several turbulence models, such as the Smagorinsky model, the wall adapting local eddy-viscosity model, and Vreman’s model have been investigated. One focus was on the applicability of the Lattice Boltzmann method to turbulent flows, considering also the interdependence between the numerical method and the LES model. Particular attention was paid to the ability of these models to correctly reproduce turbulent shear flows. Some typical infrastructure elements have been studied and compared to wind-tunnel data. The simulations were carried out on a PC cluster and on graphics processing chips. Overall, the Lattice Boltzmann method has yielded good results for turbulent flow simulations, which is documented in several benchmarks. In particular, the results for the Factorized CLB model show for the first time for a reasonably complex benchmark, that the model performs well for turbulent flows, for which an explanation is attempted.Strömungsmechaniksimulationen sind in vielen Bereichen des Ingenieurwesens bereits Standard. Für die anspruchsvollen Simulationen von Strömungen auf Gebäudeskala im Bauingenieurwesen ist dies jedoch aufgrund des hohen Aufwands und der komplexen Geometrien noch nicht der Fall. Insbesondere zeitaufgelöste dreidimensionale Simulationen wie Large Eddy Simulationen finden in der Praxis kaum Anwendung. Andererseits kann damit gerechnet werden, dass mit der zunehmender Leistungsfähigkeit von Rechnersystemen und Fortschritten bei numerischen Methoden relevante Anwendungen immer praktikabler werden. In dieser Arbeit wurde als Ausgangspunkt das Lattice Boltzmann (LB) Verfahren gewählt. Aufgrund der guten Parallelisierbarkeit eignet es sich für derart aufwändige Anwendungen besonders. Verschiedene Varianten des LB-Verfahrens, nämlich das Lattice-Bhatnagar-Gross-Krook-Verfahren , das Multiple-Relaxation-Time-Verfahren und Varianten des Kaskadierten Lattice-Boltzmann-Verfahrens (CLB), wurden implementiert und anhand von Benchmarks verglichen. Desweiteren wurden verschiedene Turbulenzmodelle, wie das Smagorinsky-Modell, das wall adapting local eddy-viscosity-Modell und das Vreman-Modell untersucht. Dabei wurde ein besonderes Augenmerk auf die Anwendbarkeit der LB-Modelle bei turbulenten Strömungen gerichtet und auch berücksichtigt, dass eine Wechselwirkung zwischen dem verwendeten LB-Modell und dem Large-Eddy-Modell vorliegt. Beispielhaft wurden dann die Strömung in und um einige Strukturen auf Gebäudeskala, bzw. entsprechender Windkanalmodelle, untersucht. Dazu wurden verteilte Rechnungen auf einem CPU-Cluster und auf Grafikkarten (GPGPUs) durchgeführt. Im Allgemeinen hat das LB Verfahren gute Ergebnisse für turbulente Strömungen geliefert. Insbesondere die Ergebnisse zum faktorisierten CLB-Modell zeigen zum ersten Mal an einem komplexen Testfall, dass dieses Modell für turbulente Strömungen gut geeignet ist, wofür auch Erklärungsansätze geliefert werden

Real-Time Simulation of Indoor Air Flow using the Lattice Boltzmann Method on Graphics Processing Unit

This thesis investigates the usability of the lattice Boltzmann method (LBM) for the simulation of indoor air flows in real-time. It describes the work undertaken during the three years of a Ph.D. study in the School of Mechanical Engineering at the University of Leeds, England. Real-time fluid simulation, i.e. the ability to simulate a virtual system as fast as the real system would evolve, can benefit to many engineering application such as the optimisation of the ventilation system design in data centres or the simulation of pollutant transport in hospitals. And although real-time fluid simulation is an active field of research in computer graphics, these are generally focused on creating visually appealing animation rather than aiming for physical accuracy. The approach taken for this thesis is different as it starts from a physics based model, the lattice Boltzmann method, and takes advantage of the computational power of a graphics processing unit (GPU) to achieve real-time compute capability while maintaining good physical accuracy. The lattice Boltzmann method is reviewed and detailed references are given a variety of models. Particular attention is given to turbulence modelling using the Smagorinsky model in LBM for the simulation of high Reynolds number flow and the coupling of two LBM simulations to simulate thermal flows under the Boussinesq approximation. A detailed analysis of the implementation of the LBM on GPU is conducted. A special attention is given to the optimisation of the algorithm, and the program kernel is shown to achieve a performance of up to 1.5 billion lattice node updates per second, which is found to be sufficient for coarse real-time simulations. Additionally, a review of the real-time visualisation integrated within the program is presented and some of the techniques for automated code generation are introduced. The resulting software is validated against benchmark flows, using their analytical solutions whenever possible, or against other simulation results obtained using accepted method from classical computational fluid dynamics (CFD) either as published in the literature or simulated in-house. The LBM is shown to resolve the flow with similar accuracy and in less time

Entropic Lattice Boltzmann Method for Moving and Deforming Geometries in Three Dimensions

Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work Dorschner et al. [11] as well as for three dimensional one-way coupled simulations of engine-type geometries in Dorschner et al. [12] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases including two-way coupling between fluid and structure, turbulence and deformable meshes. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil at a Reynolds number of Re = 40000 and finally, to access the model's performance for deforming meshes, we conduct a two-way coupled simulation of a self-propelled anguilliform swimmer. These simulations confirm the viability of the new fluid-structure interaction lattice Boltzmann algorithm to simulate flows of engineering relevance.Comment: submitted to Journal of Computational Physic

Finite Volume vs.vs. Streaming-based Lattice Boltzmann algorithm for fluid-dynamics simulations: a one-to-one accuracy and performance study

A new finite volume (FV) discretisation method for the Lattice Boltzmann (LB) equation which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard $streaming$ (ST) Lattice Boltzmann equation algorithm. To our knowledge such a systematic comparison has never been previously reported. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken as the method of choice in fluid-dynamics LB simulations. For this reason the comparative analysis is further extended to the case of realistic flows, in particular thermally driven flows in turbulent conditions. We report the first successful simulation of high-Rayleigh number convective flow performed by a Lattice Boltzmann FV based algorithm with wall grid refinement.Comment: 15 pages, 14 figures (discussion changes, improved figure readability

Numerical simulation of fluid-fluid and solid-fluid interactions: a lattice Boltzmann strategy

It is crucial to obtain a better understanding of fluid-fluid and solid-fluid interactions with several applications in science and engineering disciplines. Associating fluids such as water, alcohols, asphaltene might exist in many processes. Modeling associating fluids to explore phase equilibrium behaviors is required for proper design, operation, and optimization of various chemical and energy processes. Pseudopotential lattice Boltzmann method (LBM) can be a promising and capable mesoscopic approach to study phase transition and thermodynamic behaviors of complex fluid systems. Results of integrating the cubic equations of state (EOSs) with LBM showed a considerable deviation from experimental data for associating fluids. Cubic-plus-association (CPA) EOS is utilized in the LBM to increase the accuracy of modeling associating fluids. A global optimization approach is applied to determine the optimum association parameters of CPA EOS for water and primary alcohols in the lattice units. Maxwell equal area construction is used to verify the thermodynamic consistency. By increasing the isotropy order of gradient operator, the spurious velocities are decreased, and an extended form of CPA EOS is introduced to find proper initial densities, which increase the stabilities at low reduced temperatures. Simulating fluid flow at high Reynolds number is another aspect of an LBM study that needs further improvement. In fluid flow in porous media, specifically at tight gas reservoirs, a high flow rate might happen at pore throat. Therefore, to increase the stability of the model at high Reynolds number, the central moments collision operator is implemented in the LBM. The advantages of central moments collision operator are shown by comparing with multi relaxation time (MRT) collision operator in the double shear layers test. It is found that using a higher order of isotropy in the gradient operator can lead to a 34% reduction in spurious velocities. From the thermodynamic consistency point of view, it is concluded that collision operators can also have an impact on the consistency of the model. Furthermore, the model validation is performed by observing a straight line in the Laplace law test. Surface wettability is known as an important concept to achieve a better understanding of fluid flow and distribution in both porous and non-porous systems. Improving the solid-fluid interaction can help to have a better understanding of thermodynamics of curved interfaces. The contact angle is an important parameter to study the multiphase fluid flow in various systems such as porous media and membranes. It helps to design better production, separation, treatment, and reaction processes in different applications. In order to increase the accuracy and reliability of the model for simulation of the surface wettability and absorption, a new solid-fluid interaction in the pseudopotential approach is introduced. Usually, the surface wettability is reported by the contact angle, which is measured by fitting a circle on the drop. Because the circle is a constant curvature shape, it is not suitable to consider the disjoining pressure. A new strategy is presented based on the Smoothing Splines to measure the contact angle without considering a constant curvature shape of the interface profile. The new solid-fluid interaction exhibits the capability of simulating extreme non-wetting surfaces without detaching the drop. The probability histogram of the density domain appears to be a reliable tool to measure the phase density in the presence of a surface. The results of the current research have a wide range of applications in energy and environment, such as simulation of fluid flow in porous systems (e.g., shale reservoirs and membranes). Pores and fractures are large in conventional permeable media and pressure-drive convective flow is applicable in the framework of continuum flow. Shale reservoir have fine grains and pores in the range on nanometer where fluid molecular distribution is inhomogeneous and surface adsorption may be significant. Coupling the introduced method with nucleation theory provide a powerful tool to simulate asphaltene precipitation in the porous media. The presence of water component as an associating fluid in some biological processes such as blood coagulation makes the presented model an effective tool to simulate those processes