72 research outputs found

    Hybrid discretizations of the Boltzmann equation for the dilute gas flow regime

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    New hybrid numerical model allows large scale flow simulations in high-tech production equipmen

    Thermal fluctuations and boundary conditions in the lattice Boltzmann method

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    The lattice Boltzmann method is a popular approach for simulating hydrodynamic interactions in soft matter and complex fluids. The solvent is represented on a discrete lattice whose nodes are populated by particle distributions that propagate on the discrete links between the nodes and undergo local collisions. On large length and time scales, the microdynamics leads to a hydrodynamic flow field that satisfies the Navier-Stokes equation. In this thesis, several extensions to the lattice Boltzmann method are developed. In complex fluids, for example suspensions, Brownian motion of the solutes is of paramount importance. However, it can not be simulated with the original lattice Boltzmann method because the dynamics is completely deterministic. It is possible, though, to introduce thermal fluctuations in order to reproduce the equations of fluctuating hydrodynamics. In this work, a generalized lattice gas model is used to systematically derive the fluctuating lattice Boltzmann equation from statistical mechanics principles. The stochastic part of the dynamics is interpreted as a Monte Carlo process, which is then required to satisfy the condition of detailed balance. This leads to an expression for the thermal fluctuations which implies that it is essential to thermalize all degrees of freedom of the system, including the kinetic modes. The new formalism guarantees that the fluctuating lattice Boltzmann equation is simultaneously consistent with both fluctuating hydrodynamics and statistical mechanics. This establishes a foundation for future extensions, such as the treatment of multi-phase and thermal flows. An important range of applications for the lattice Boltzmann method is formed by microfluidics. Fostered by the “lab-on-a-chip” paradigm, there is an increasing need for computer simulations which are able to complement the achievements of theory and experiment. Microfluidic systems are characterized by a large surface-to-volume ratio and, therefore, boundary conditions are of special relevance. On the microscale, the standard no-slip boundary condition used in hydrodynamics has to be replaced by a slip boundary condition. In this work, a boundary condition for lattice Boltzmann is constructed that allows the slip length to be tuned by a single model parameter. Furthermore, a conceptually new approach for constructing boundary conditions is explored, where the reduced symmetry at the boundary is explicitly incorporated into the lattice model. The lattice Boltzmann method is systematically extended to the reduced symmetry model. In the case of a Poiseuille flow in a plane channel, it is shown that a special choice of the collision operator is required to reproduce the correct flow profile. This systematic approach sheds light on the consequences of the reduced symmetry at the boundary and leads to a deeper understanding of boundary conditions in the lattice Boltzmann method. This can help to develop improved boundary conditions that lead to more accurate simulation results

    Flowing matter

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    This open access book, published in the Soft and Biological Matter series, presents an introduction to selected research topics in the broad field of flowing matter, including the dynamics of fluids with a complex internal structure -from nematic fluids to soft glasses- as well as active matter and turbulent phenomena.Flowing matter is a subject at the crossroads between physics, mathematics, chemistry, engineering, biology and earth sciences, and relies on a multidisciplinary approach to describe the emergence of the macroscopic behaviours in a system from the coordinated dynamics of its microscopic constituents.Depending on the microscopic interactions, an assembly of molecules or of mesoscopic particles can flow like a simple Newtonian fluid, deform elastically like a solid or behave in a complex manner. When the internal constituents are active, as for biological entities, one generally observes complex large-scale collective motions. Phenomenology is further complicated by the invariable tendency of fluids to display chaos at the large scales or when stirred strongly enough. This volume presents several research topics that address these phenomena encompassing the traditional micro-, meso-, and macro-scales descriptions, and contributes to our understanding of the fundamentals of flowing matter.This book is the legacy of the COST Action MP1305 “Flowing Matter”

    KINETICALLY CONSISTENT THERMAL LATTICE BOLTZMANN MODELS

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    The lattice Boltzmann (LB) method has developed into a numerically robust and efficient technique for simulating a wide variety of complex fluid flows. Unlike conventional CFD methods, the LB method is based on microscopic models and mesoscopic kinetic equations in which the collective long-term behavior of pseudo-particles is used to simulate the hydrodynamic limit of a system. Due to its kinetic basis, the LB method is particularly useful in applications involving interfacial dynamics and complex boundaries, such as multiphase or multicomponent flows. However, most of the LB models, both single and multiphase, do not satisfy the energy conservation principle, thus limiting their ability to provide quantitatively accurate predictions for cases with substantial heat transfer rates. To address this issue, this dissertation focuses on developing kinetically consistent and energy conserving LB models for single phase flows, in particular. Firstly, through a procedure similar to the Galerkin method, we present a mathematical formulation of the LB method based on the concept of projection of the distributions onto a Hermite-polynomial basis and their systematic truncation. This formulation is shown to be capable of approximating the near incompressible, weakly compressible, and fully compressible (thermal) limits of the continuous Boltzmann equation, thus obviating the previous low-Mach number assumption. Physically it means that this formulation allows a kinetically-accurate description of flows involving large heat transfer rates. The various higher-order discrete-velocity sets (lattices) that follow from this formulation are also compiled. The resulting higher-order thermal model is validated for benchmark thermal flows, such as Rayleigh-Benard convection and thermal Couette flow, in an off-lattice framework. Our tests indicate that the D2Q39-based thermal models are capable of modeling incompressible and weakly compressible thermal flows accurately. In the validation process, through a finite-difference-type boundary treatment, we also extend the applicability of higher-order la ttices to flow-domains with solid boundaries, which was previously restricted. Secondly, we present various off-lattice time-marching schemes for solving the discrete Boltzmann equation. Specifically, the various temporal schemes are analyzed with respect to their numerical stability as a function of the maximum allowable time-step . We show that the characteristics-based temporal schemes offer the best numerical stability among all other comparable schemes. Due to this enhanced numerical stability, we show that the usual restriction no longer applies, enabling larger time-steps, and thereby reducing the computational run-time. The off-lattice scheme were also successfully extended to higher-order LB models. Finally, we present the algorithm and single-core optimization techniques for a off-lattice, higher-order LB code. Using simple cache optimization techniques and a proper choice of the data-structure, we obtain a 5-7X improvement in performance compared to a naive, unoptimized code. Thereafter, the optimized code is parallelized using OpenMP. Scalability tests indicate a parallel efficiency of 80% on shared-memory systems with up to 50 cores (strong scaling). An analysis of the higher-order LB models also show that they are less memory-bound if the off-lattice temporal schemes are used, thus making them more scalable compared to the stream-collide type scheme

    A high-order hybridizable discontinuous Galerkin method with fast convergence to steady-state solutions of the gas kinetic equation

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    The mass flow rate of Poiseuille flow of rarefied gas through long ducts of two-dimensional cross-sections with arbitrary shape is critical in the pore-network modeling of gas transport in porous media. Here, for the first time, the high-order hybridizable discontinuous Galerkin (HDG) method is used to find the steady-state solution of the linearized Bhatnagar–Gross–Krook equation on two-dimensional triangular meshes. The velocity distribution function and its traces are approximated in piecewise polynomial spaces (of degree up to 4) on the triangular meshes and mesh skeletons, respectively. By employing a numerical flux that is derived from the first-order upwind scheme and imposing its continuity weakly on the mesh skeletons, global systems for unknown traces are obtained with fewer coupled degrees of freedom when compared to the original discontinuous Galerkin formulation. To achieve fast convergence to the steady-state solution, a diffusion-like equation for flow velocity, which is asymptotic-preserving into the fluid dynamic limit, is solved by the HDG simultaneously on the same meshes. The proposed HDG-synthetic iterative scheme is proved to be accurate and efficient. Specifically, for flows in the near-continuum regime, numerical simulations have shown that, to achieve the same level of accuracy, our scheme could be faster than the conventional iterative scheme by two orders of magnitude, also it is faster than the synthetic iterative scheme based on the finite difference discretization in the spatial space by one order of magnitude. In addition, the implicit HDG method is more efficient than an explicit discontinuous Galerkin gas kinetic solver, as well as the implicit discontinuous Galerkin scheme when the degree of approximating polynomial is larger than 2. The HDG-synthetic iterative scheme is ready to be extended to simulate rarefied gas mixtures and the Boltzmann collision operator

    Modélisation des écoulements de gaz raréfiés au travers de filtres fibreux par la méthode de Boltzmann sur réseau

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    RÉSUMÉ: Les particules fines suspendues dans l’air (aussi nommées aérosols) sont nocives pour la santé humaine et pour l’environnement. La filtration des aérosols (ou la séparation de ces particules de l’air) est donc un procédé d’une importance cruciale. Les filtres fibreux sont généralement choisis pour leur haute performance et leur compacité. L’ajout de nanofibres (<1 μm) déposées sur une couche de microfibres ou mélangées à des microfibres a été proposé pour améliorer ces filtres. La théorie de la fibre unique est souvent utilisée pour prédire la performance des filtres à aérosols. Cependant, cette théorie prend pour acquis que les fibres d’un filtre sont toutes du même diamètre et ignore donc les impacts potentiels de la structure multicouche. La simulation numérique directe des écoulements gazeux au travers de milieux fibreux doit être utilisée pour tenir compte des interactions entre les fibres. Or, les effets de raréfaction qui apparaissent autour des nanofibres doivent être considérés pour prédire quantitativement la performance des milieux filtrants.----------ABSTRACT: Suspensions of fine particles (also called aerosols) are harmful to human health and the environment. The filtration of airborne particles (or the separation of these particles from the air) is therefore a process of crucial importance. Fibrous filters are generally chosen for their high performance and compactness. The addition of nanofibers (<1 μm) deposited on a layer of microfibers or mixed with microfibers has been proposed to improve these filters. The single fiber theory is often used to predict the performance of aerosol filters. However, this theory assumes that the fibers of a filter are all the same diameter and therefore ignores the potential impacts of the multilayer structure. Direct numerical simulation of gas flows through fibrous media must be used to account for the interactions between the fibers. However, the rarefaction effects that occur around nanofibers must be considered to quantitatively predict the performance of the filter media

    Review of Boundary Conditions and Investigation Towards the Development of a Growth Model: a Lattice Boltzmann Method Approach

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    El mètode de Lattice Boltzmann (LBM) es una tècnica computacional de simulació dinàmica de fluids que esta guanyant popularitat degut a les seves propietats inherents: pot treballar amb geometries complexes amb relativa facilitat, es fàcil de implementar computacionalment i pot ser utilitzat de forma efectiva amb eines de alta paralel·lització computacional. Tot i això el mètode encara no està totalment establert en la comunitat cientifica degut a la seva relativa primerenca aparició. Un conegut tòpic que està sota investigació activa és el desenvolupament de condicions de frontera efectives, especialment les no-reflexives. Podem trobar a la literatura diverses propostes de condicions de frontera no-reflexives per LBM. Tot i això, no hi ha massa investigació empresa sobre el impacte físic de utilitzar una condició de frontera reflexiva o no-reflexiva més enllà dels tests de condició de frontera. Per altra banda, el LBM també és capaç de recuperar la equació de transport de advecció-difusió utilitzant un escalar passiu. L'estudi de les plaquetes en la sang és un estudi molt actiu, i una de les tècniques utilitzades en LBM per modelitzar-ne el seu transport es a través de un escalar passiu. Les plaquetes son una peça clau en la coagulacio, que pot arribar a taponar una artèria quan la coagulació passa en una arteria amb arterioesclerosis severa. Les plaquetes també experimenten un moviment lateral cap a les parets, anomenada marginació, que augmenta de forma natural la seva capacitat de coagulació. La memòria de la tesi consisteix en dues parts distingides. Primerament, es presenten els resultats d'un estudi paramètric per analitzar el impacte físic de les reflexions artificials que es produeixen en un flux que passa per un obstacle dins d'un canal. En segon lloc, es desenvolupa un model de transport per a les plaquetes basat en la tècnica de la doble funció de distribució en LBM, es reprodueix el procés de la marginació i es prepara un grup de eines per a desenvolupar un model de creixement que pugui reproduir un episodi de trombosis en una artèria coronaria.l método lattice Boltzmann (LBM) es una técnica de computación dinámica de fluidos (CFD) que está ganando popularidad rápidamente debido a sus inherentes propiedades: trata formas geometricas con relativa facilidad, es computacionalmente fácil de implementar y se puede usar con herramientas de paralelización de forma eficaz. No obstante, este método no está enteramente establecido en la comunidad científica debido a su relativa temprana aparición. Un tema común que aún se encuentra en investigación activa es el estudio y desarrollo de condiciones de frontera efectivas, en especial las no-reflexivas. Se puede encontrat en la literatura varias propuestas de condiciones de frontera no-reflexivas, pero no hay mucha investigación hecha sobre el impacto físico que se genera al condiciones de frontera reflexivas o no-reflexivas mas allá de los test para las condiciones de frontera. Por otra parte, el método de lattice Boltzmann también puede desarrollar simulaciones basadas en la equación de advección-diffusion usando un escalar pasivo. Una temática muy activa que considera esta técnica es el transporte de las plaquetas en la sangre. Ellas son la clave del proceso de coagulación, pueden llegar a taponar una arteria que tenga arterioesclerosis severa. Adicionalmente, las plaquetas presentan un desplazamento lateral espontáneo, llamado marginación, y generan un exceso de concentración de plaquetas cerca de las paredes de la arteria. El reporte de la tesis consiste en dos partes diferenciadas. Primero se presenta un estudio parametrico en el cual se analiza y caracteriza el impacto the las reflexiones producidas en un flujo en un canal con un obstáculo en el medio. Después, se desarrolla un modelo de plaquetas basado en la doble dfunción de distribución y reproducimos el efecto de marginación de las plaquetas. Adicionalmente preparamos un conjunto de herramientas computacionals para desarrollar un modelo de crecimiento que se asemeje a un episodio de trombosis en una arteria coronaria.The lattice Boltzmann method (LBM) is a computational fluid dynamics technique that is rapidly earning popularity due to its inherent properties: it deals with complex geometries with relative ease, it is computationally easy to implement and it can be effectively used with massive parallel computing tools. However, the method is still not entirely established in the scientific community due to its relatively early appearance. One known topic that is still under active research are the study and development of effective boundary conditions, specially non-reflecting ones. We can find on the literature several proposals of non-reflective boundary conditions for LBM. However, there is not much conducted research about the physical impact of using a reflective or a non-reflective approach on a simulation beyond the boundary tests. On the other hand, the LBM is also capable to able to hold the advection-diffusion transport equation by means of a passive scalar. One very active topic is the study of the blood platelet transport. Platelets are the cornerstone of the coagulation and this latter phenomenon can occlude an artery when platelets are activated in an atherosclerotic artery, which is called thrombosis. Platelets also experiment a spontaneous migration, called margination, to the walls that naturally enhance their performance. The thesis report consists on two distinct parts. Firstly, we present the results of a parametric study to analyze the physical impact of the spurious reflections that occur on a flow past a square obstacle in a confined channel. Secondly, we develop a transport model for platelets in the LBM based on the double distribution technique and we reproduce the margination of platelets and we prepare a set of tools to develop a growth model to resemble a thrombosis event in a coronary artery

    Lattice-Boltzmann Modelling of Immiscible Fluid Displacement in Geologic Porous Media

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    Over the past two decades, multicomponent lattice-Boltzmann (LB) modelling has become a popular numerical technique to study the porous medium systems. For this technique to become a mature platform at a production level and to solve realistic problem that can be readily incorporated in the digital core analysis services for the oil and gas industries, there are still some challenges to resolve. This thesis intends to resolve some of issues confronted by the LB community. The first part of the thesis investigates the impact of the fundamental trade-off between image resolution and field of view on LB modelling. This is of practical value since 3D images of geological samples rarely have both sufficient resolution to capture fine structure and sufficient field of view to capture a full representative elementary volume of the medium. To optimise the simulations, it is important to know the minimum number of grid points that LB methods require to deliver physically meaningful results, and allow for the sources of measurement uncertainty to be appropriately balanced. We choose two commonly used multicomponent LB models, Shan-Chen and Rothman-Keller models, and study the behaviour of these two models when the phase interfacial radius of curvature and the feature size of the medium approach the discrete unit size of the computational grid. Both simple, small-scale test geometries and real porous media are considered. Models' behaviour in the extreme discrete limit is classified ranging from gradual loss of accuracy to catastrophic numerical breakdown. Based on this study, we provide guidance for experimental data collection and how to apply the LB methods to accurately resolve physics of interest for two-fluid flow in porous media. Resolution effects are particularly relevant to the study of low-porosity systems, including fractured materials, when the typical pore width may only be a few voxels across. The second part of the thesis explores the two-fluid displacement mechanism, especially the Haines jump dynamics and associated snap-off during drainage, by using a novel flux boundary condition, which is numerically more stable, and can more realistically replicate experiments given a prescribed capillary number. Irreversible events such as Haines jump in multiphase flow is what ultimately determines the hysteric behaviour of the porous medium systems. The high temporal resolution of LB methods makes it a suitable candidate to capture the dynamics of fast events (e.g. Haines jump in millisecond). We study the impacts of both the geometries of porous medium using persistent homology and the dynamic factors of fluids (i.e. viscosity ratio and capillary number) on the occurrence and frequency of snap-off events during drainage
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