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## Multiscale fluid dynamics with the Lattice Boltzmann method |

“Deformable cellular suspension in biological flows - progress and challenges in multiscale analysis with LBM” The advantages and challenges in multiscale analysis of suspension flows with lattice Boltzmann (LB) method based on our experience will be discussed by considering three applications – cellular blood flow, platelet damage in mechanical heart valves, and rheology of deformable slender bodies. Analysis of blood flow with realistic hematocrit requires direct numerical simulation of individual red blood cells (RBCs) immersed in Newtonian blood plasma with hemoglobin within. A coarse-grained spectrin-link (SL) RBC membrane model is coupled with LB flow solver to capture RBC dynamics in isolation and in dense suspension of O(1000) RBCs at realistic hematocrit values. Validation results include experimental comparisons with results for isolated RBCs tumbling, tank-treading, deforming in the wheel configuration, and parachuting in a microvessel-sized rigid tube. The rheology of blood is analyzed via LB-SL simulations of RBC suspensions at physiological concentration. The results characterize the effect of the RBC d formation on the viscosity, normal stress differences, and particle pressure. Applications will be discussed. Studies have shown that high shear stress and large recirculation regions have strong impact on thromboembolic complications in Bileaflet mechanical heart valves (BMHV) particularly in the hinge area. The LB method with external boundary force (LB-EBF) is implemented to simulate the flow and capture the dynamics and the surface shear stress of the platelets with realistic geometry in the hinge of two BMHVs - 23mm St. Jude Medical (SJM) regent with different and the 23mm CarboMedics (CM) valves. Progress with this method and the need for further development will be discussed. If time allows, application of the LB-EBF method to deformable slender bodies such as fiber suspension will be discussed. Cyrus K Aidun, G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, USA ---
“Large scale Lattice Boltzmann simulations in irregular geometries:issues and results on standand and non-conventional Hw/Sw architectures” We describe our experience in the development of a flexibile, high performance parallel Lattice Boltzmann code for the simulation of bio-fluids in irregular geometries. Issues related to load balancing and communication pattern are described along with the solutions we devised and the results obtained both on standard platforms (like the IBM BlueGene) and, more recently, on (large) clusters of GPU. Massimo Bernaschi, National Research Council of Italy. ---
“Integrating a LB flow solver into a distributed multi-scale simulation environment for medical physics” ---
“Large- and small-scales statistics in numerical simulations of stratified Rayleigh-Taylor systems using thermal Lattice Boltzmann Methods” Abstract: The parameterization of small-scale turbulent fluctuations in convective systems and in the presence of strong stratification is a key issue for many applied problems in oceanography, atmospheric science and planetology. In the presence of stratification, one needs to cope with bulk turbulent fluctuations and with inversion regions, where temperature, density --or both-- develop highly nonlinear mean profiles due to the interactions between the turbulent boundary layer and the unmixed --stable-- flow above/below it. We present a second order closure able to cope {\it simultaneously} with both bulk and boundary layer regions, and we test it against high-resolution state-of-the-art 2D numerical simulations in a convective and stratified belt for values of the Rayleigh number, up to $Ra \sim 109$. Data are taken from a Rayleigh-Taylor system confined by the existence of an adiabatic gradient. ---
“The application of the lattice Boltzmann method to modelling multi-component flows and bio-reactors” In the first part of the talk we present an extension of the lattice Boltzmann (lB) method to recover the hydrodynamics of multi-component immiscible ﬂuids using an essentially local and explicit algorithm. The local nature of the algorithm makes the method highly scalable when used in high performance parallel-computing. The method is demonstrated by modelling the flow of a fluid containing a large number of individually immiscible drops. Comparisons are made of the emergent non-Newtonian behaviour with a power-law ﬂuid model. In the second part of the talk an LB model of the flow in a perfusion bone-tissue bioreactor is presented. The model includes a complete formulation of transport with fully coupled convection-diffusion and scaffold cell attachment. It also includes the experimentally determined internal (poly-L-lactic acid (PLLA)) scaffold boundary, together with the external vessel and flow-port boundaries. Our findings, obtained using a parallel lB algorithm, relate to (i) whole-device, steady-state flow and species distribution and (ii) the properties of the scaffold. In particular the results identify which elements of the problem may be addressed by coarse grained methods such as the Darcy approximation and those which require a more complete description. The work demonstrates that appropriate numerical modelling will make a key contribution to the design and development of large scale bioreactors. Timothy J Spencer, Ian Halliday and Chris M Care - Materials and Engineering Research Institute, Sheﬃeld Hallam University, Howard Street, Sheﬃeld S1 1WB, UK ---
“ A Methodology for Multiscale-Multiscience Lattice-Boltzmann Simulations” Multiscale, multiscience applications are becoming more and more important in order to solve modern computational challenges. propose a theoretical framework, together with a software implementation, to describe and develop multiscale Lattice-Boltzmann simulations. This approach will be illustrated in the case of a biomedical application, i.e. the process of restenosis in stented arteries, which combines fluid flow, diffusion and biology at different scales. Bastien Chopard, University of Geneva, Switzerland ---
“Parallel space-time approach to turbulence: computation of unstable periodic orbits and the dynamical zeta function” We present a novel methodology that proposes to utilize petascale resources in the computation of turbulent quantities from first principles. The method is based on a spacetime variational approach that computes the relevant unstable periodic orbits (UPOs) in turbulent flow governed by the Navier-Stokes equations. To implement this we have developed a fully parallel software package, called HYPO4D, based on the lattice-Boltzmann method for fluid simulation, which has an impressive parallel performance. Extensive numerical simulations performed on a range of supercomputing resources in both Europe and the USA, with special emphasis on the Blue Gene/P machines Intrepid, at Argonne National Laboratory, and JUGENE, at the Juelich Supercomputing Centre, have demonstrated the validity of this approach, with the computation of the first UPOs in such high-dimensional systems. We also demonstrate the application of these ideas to a test case, the Lorenz attractor, and discuss the prospects of this approach, which allows for an exact computation of turbulent quantities in dynamical systems, thus bypassing the inherently statistical error distribution that arises in more conventional approaches. ---
“eroacoustic simulation of slender gap resonance and trailing edge noise using the Lattice Boltzmann method” ---
"Lattice Boltzmann modelling of collisional plasmas" We present a summary of recent developments in lattice Boltzmann algorithms for extended magnetohydrodynamic models that offer more realistic descriptions of collisional plasmas. Particular areas include Braginskii magnetohydrodynamics, which describes strongly magnetised plasmas in which the viscous stress is predominantly directed along magnetic field lines, and the implementation of the current-dependent resistivities used to model plasma microturbulence and in magnetohydrodynamic large eddy simulations. We also show applications of the same algorithm for simulating electromagnetic waves in media. ---
“Drag and lift on random assemblies of wall-attached spheres in low-Reynolds number shear flow” Direct numerical simulations of the shear flow over assemblies of uniformly sized, solid spheres attached to a flat wall have been performed using the lattice-Boltzmann method. The random sphere assemblies comprised monolayers, double layers, and triple layers. The Reynolds number based on the sphere radius and the overall shear rate was much smaller than one. The results were interpreted in terms of the drag force (the force in streamwise direction) and lift force (the force in wall-normal direction) experienced by the spheres as a function of the denseness of the bed and the depth of the spheres in the bed. The average drag and lift force decay monotonically as a function of the surface coverage of the spheres in the top layer of the bed. The sphere-to-sphere variation of the drag and lift force is significant due to interactions between spheres via the interstitial fluid flow.
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“Simulating the dynamics of a single polymer chain in solution: Lattice Boltzmann vs Brownian Dynamics” One possible way of simulating the dynamics of Brownian particles in solution is via dissipative coupling of such particles to a Lattice Boltzmann background fluid, and adding Langevin noise to both parts. This method however competes with the established approach of implementing a hydrodynamic interaction tensor in a Brownian Dynamics simulation. After a brief introduction into both methods, a benchmark calculation is presented, in which the dynamics of a single flexible polymer chain in good solvent is studied. Very good agreement between both methods is found after proper extrapolation to the infinite-volume limit, provided that the fluid is thermalized with respect to all non-conserved degrees of freedom, i.e. with respect to both the stresses and the kinetic modes. For this particular system, Brownian Dynamics is found to be computationally more efficient. However, it is argued that this situation is reversed if one rather studies a semidilute system. See also: Tri T. Pham, Ulf D. Schiller, J. Ravi Prakash, and B. Duenweg, J. Chem. Phys. 131, 164114 (2009). ---
“Colloidal particles in multiphase flow” Particle stabilized emulsions are ubiquitous in the food and cosmetics industry, but our understanding of the influence of microscopic fluid-particle and particle-particle interactions on the macroscopic rheology is still limited. In this contribution we present a simulation algorithm based on a multicomponent lattice Boltzmann model to describe the solvents combined with a molecular dynamics solver for the description of the solved particles. The model allows a wide variation of fluid properties and arbitrary contact angles on the particle surfaces. We study the parameter dependence of the model and demonstrate its applicability by studying the formation and rheology of a ``bicontinuous interfacially jammed emulsion gel'' (bijel) and of a ``Pickering emulsion''. ---
“waLBerla: A Software Framework for CFD Applications on 300.000 Compute Cores” In the era of multicore CPUs, GPU computing and large scale supercomputers, a scientific software framework should exploit these machines efficiently. While utilizing processors in a reasonable way for numerical kernel routines is complex and time-consuming, this is even more difficult and time consuming for large software frameworks, like the waLBerla project. waLBerla is our implementation of a massively parallel lattice Boltzmann fluid solver with various add-on applications. In this talk i will describe the framework shortly and discuss free-surface flows, particulate flows and GPU computing. ---
"Simplified particulate model for coarse-grained hemodynamics simulations". Human blood flow is a multi-scale problem: in first approximation, blood is a dense suspension of plasma and deformable red cells. Physiological vessel diameters range from about one to thousands of cell radii. Current computational models either involve a homogeneous fluid and cannot track particulate effects or describe a relatively small number of cells with high resolution, but are incapable to reach relevant time and length scales. Our approach is to simplify much further than existing particulate models. We combine well established methods from other areas of physics in order to find the essential ingredients for a minimalist description that still recovers hemorheology. These ingredients are a lattice Boltzmann method describing rigid particle suspensions to account for hydrodynamic long range interactions and---in order to describe the more complex short-range behavior of cells---anisotropic model potentials known from molecular dynamics simulations. Paying detailedness, we achieve an efficient and scalable implementation which is crucial for our ultimate goal: establishing a link between the collective behavior of millions of cells and the macroscopic properties of blood in realistic flow situations. We present our model and demonstrate its applicability to various flow configurations. ---
“Direct numerical simulations with lattice Boltzmann method” In this talk, we shall discuss the current status of the lattice Boltzmann method as an alternative for the direct numerical simulation (DNS) of high Reynolds number flow phenomena. After reviewing a recent work on 3D DNS of turbulent vortex flow with higher-order LBGK scheme [Chikatamarla et al, J. Fluid Mech. (2010)], we shall introduce recent enhancements of the LBGK scheme and illustrate the advantage of these methods in two dimensional simulations. Open questions which are need to be addressed in order to put lattice Boltzmann methods as an alternative DNS shall also be listed. Ilya Karlin, Shyam Chikatamarla, Daniel Lycett-Brown ---
“LB-Methods for Engineering CFD: potentials & problems” ---
“Modeling Tumor Blood Vessel Dynamics” Anti-angiogenic therapies can normalize tumor blood vessels, making them structurally and functionally more efficient at delivering chemotherapeutics to cancer cells. For example, blocking vascular endothelial growth factor (VEGF, the major vascular growth factor in tumors) decreases vascular diameters and vascular density and restores endothelial barrier function, making the vasculature less leaky. Unfortunately, normalizing tumor vessels using anti-VEGF drugs in the clinic has proven inconsistent. This is largely due to our lack of understanding of the dynamics of vascular normalization, and a failure to identify the optimal timing for application of the chemotherapeutic agent. We present a mathematical model to investigate the influence of various structural and functional vascular parameters on drug delivery. The model is based on a lattice Boltzmann flow solver with additional production, consumption and transport of oxygen and VEGF. The model includes realistic, local oxygen release by convecting red blood cells and modulation of vascular structures driven by endothelial shear stress and VEGF levels. Our results show that network topology and vascular permeability can be modulated to enhance drug delivery. ---
“Numerical simulations of fracture dissolution” In common rock formations, particularly limestone, aqueous CO2 dissolves the surrounding rock matrix, leading to an increase in permeability. Under some conditions, there is a feedback mechanism, which tends to amplify initially small variations in permeability, leading to the formation of deep channels through which almost all the fluid flows. This is thought to be the origin of the spectacular underground caves that can occur in limestone and other formations. It is also of importance in certain engineering applications; for example the stability of dams or predicting the length of time sequestered CO2 might be retained in geological formations. Our investigation uses both theoretical and computational tools to study the dissolution of individual fractures where most of the flow and transport in rocks occurs. Linear stability analysis shows that fracture dissolution is inherently unstable, even in the simplest geometry (a planar fracture bounded by smooth walls). During dissolution, deep channels of eroded material develop from the initial instability in the front. These channels interact, competing for the available flow, and eventually the growth of the shorter channels ceases. Thus the number of channels decreases with time while the characteristic distance between them increases, which leads to a scale-invariant, powerlaw distribution of channel lengths. This flow focusing is an important mechanism for allowing deep penetration of the reactant into the fracture system. Numerical simulations are the main means we have for investigating the complex interactions for flow, transport, and chemical reactions. I will present results from two and three dimensional simulations of fracture dissolution and explain how we use these results to try to build models of dissolution pattern formation. The fluid dynamics in the pore spaces is determined from a lattice-Boltzmann model, which can be very efficient in irregular geometries. I will describe a simple LB model for time-independent Stokes flow and some recent results attempting to obtain a rapid solution to the steady-state flow problem. I will also discuss problems in using lattice-Boltzmann methods for the convection-diffusion equation. Tony Ladd, Chemical Engineering Department, University of Florida, Gainesville, Florida ---
"Heterogeneous Multiscale Simulations of Suspension Flow using LBM" The macroscopically emergent rheology of suspensions is dictated by details of fluid-particle, and particle-particle interactions. For systems where the typical spatial scale on the particle level is much smaller than that of macroscopic properties the scales can be split. We present a hierarchical multi-scale method (HMM) approach to macroscopic suspension flow in which at the macro-scale the suspension is treated as a non-Newtonian fluid. The local shear rate and particle volume fraction are input to a simulation of fully resolved suspension microdynamics. Measurements of the apparent viscosity and shear-induced diffusivities are then used to complete the information needed in the constitutional relations on the macroscopic level. On both levels the lattice-Boltzmann method (LBM) is applied to model the fluid phase and coupled to Lagrangian representations of the solid phase. Down- and upward mapping of viscosity and diffusivity related quantities will be discussed as well as information exchanged between the phases on both scales. Temporal scale splitting between viscous and diffusive dynamics has also been exploited to accelerate the macroscopic equilibration dynamics. Additionionally, Galileian and rotational invariance allows to make very efficient use of a database with extra/inter-polation functionality, again reducing the computational effort by factors of several orders of magnitude. The HMM suspension model is applied to the simulation of a 2-dimensional flow through a straight channel of macroscopic width. The equilibration dynamics of flow and volume fraction profiles and equilibrium profiles of volume fraction, diffusivity, velocity, shear rate, and viscosity are discussed. We show that the proposed HMM model not only reproduces experimental findings for low Reynolds numbers but also predicts additional dependencies introduced by shear-thickening effects not covered by existing macroscopic suspension flow models. ---
“Role of red blood cells in large-scale blood dynamics” We have undertakne the modeling and simulation of blood by the concurrent handling of plasma, via the Lattice Boltzmann method, and red blood cells, via an ad-hoc cellular dynamics. The level of modeling detail is sufficient to describe phenomena of potential physiological and clinical significance. Large-scale simulations in fully blown coronary systems provide a wealth of novel information about the erratic motion of red blood cells, and their structural and dynamical heterogeneities. The data show that strong modulations of endothelial shear stress results from the uneven distribution of red blood cells with implications for the local properties of blood flows. Several interesting new patterns emerge as a result of the flow-induced noise, providing new clues to the uneven distribution of red blood cells in vessels of different size. ---
“Mesoscale modeling of charged and uncharged dynamic of complex fluids” I will describe how to combine a lattice Boltzmann treatment for fluid flow of binary and charged mixtures. In particular, I will analyze how this approach can be used to study the electrokinetics of charged suspensions, and will discuss how the kinetic approach underlying the lattice Boltzmann can be exploited to described the transport properties of charged tracers. For uncharged mixtures I will analyze how thermal fluctuations can be included consistently and special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level. In this case the simulate approach can be regarded as a method for the solution of the model H fluctuating hydrodynamic equations for binary mixtures . The method is benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytic and numerical results. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations. ---
“Droplets dynamics and breakup in turbulent flows” Turbulent emulsions are of relevance to many Natural and industrial flows alike. In order to study the statistical properties of droplets deformation and breakup in turbulence we perform high resolution numerical simulations of a multicomponent flow composed by two fluid with equal density. We aim at investigating the interplay between turbulent fluctuations and surface tension. The flow is solved in a cubic periodic box with a stirring at the largest scales in order to realize an homogeneous and isotropic turbulent flow field. The numerical simulations are performed by means of a fully-parallel Lattice Boltzmann code where the two fluid components are described by means of a Shan-Chen model without need for explicit interface tracking. Our numerical experiment allow to investigate e.g. the probability distribution function of droplet radii and the physics of the exchange of energy between surface and fluid fluctuations. We present preliminary results for a selected number of problem parameters. ---
“Finite size Bubbles/Droplets in heat flow with the Lattice Boltzmann Method” Rayleigh-Bčnard (RB) convection the buoyancy of a fluid heated from below and cooled from above is a classical problem in fluid dynamics. Various situations in this context also involve convection in the presence of phase change, e.g. condensing vapors and boiling liquids. In this talk I will present a novel numerical approach for multicomponent/multiphase flows in the framework of the Lattice Boltzmann Method for complex fluids. The method is inspired by the well known Shan-Chen model for non ideal fluids and further extended to take into account temperature dynamics. The equilibrium properties of the lattice model model are shown to posses the correct thermodynamic background and able to model adequately the phase transition properties in single specie fluids. The method is finally applied to the problem of boiling/condensation in presence of convection triggered by an external temperature gradient and some preliminary results are discussed. ---
Talk 1: “Physical modeling of multiphase flow with lattice Boltzmann method” In this presentation, the non-ideal gas lattice Boltzmann (LB) model [Shan & Chen, Phys. Rev. E, 47, 1815, (1993)] is re-examined in the perspective of the kinetic theoretical framework. The emphasis is more on the model’s physical justification than the practicality which will be reviewed in a separate presentation. We shall discuss the underlying intuition, the new derivation from classic kinetic theory and statistical physics, and certain actively debated issues around the model. Talk 2: “The multiphase lattice Boltzmann model in engineering applications” In this presentation, certain basics of a recently developed prototype of a lattice Boltzmann multiphase code based on the commercial PowerFLOW software will be introduced. We shall present the fundamentals of the PowerFLOW architecture, the newly added multiphase/multi-component features, examples of validation and application, and options in future development. The aim of the talk is to foster a discussion on the industrial needs in complex fluid CAE and how those needs can be met by the development effort of the lattice Boltzmann community. ---
“Tackling multi-cubed problems in food processing with use of Lattice Boltzmann”
Understanding the physics occurring during the processing of food materials is a challenging problem. We call this a multi-cubed problem, as a) food is a multiphase material, b) the processing involves multiphysics, and c) it is a multiscale problem. To meet this challenge we are working on multiscale simulation frameworks, which includes Lattice Boltzmann - particularly at the meso-level. In the workshop we will discuss the multiscale framework on 1) particle suspensions flowing in narrow confinements (representing milk or beer in fractionation applications), and 2) moisture migration in hygroscopic porous food materials (representing soup vegetables during hydration or meat during cooking). Ruud van der Sman - Wageningen University. ---
“Matching Lattice-Boltzmann algorithms with present and future multi-core processors and massively parallel computer” ---
“Adopting and Adapting LB Technqiues for ChemE Applications” ---
“Simulation of fluid-particle interactions using CFD: comparison with LBM” ---
“Lattice Boltzmann simulations of complex fluids” An overview of research activities of the complex fluid group at the university of Bochum is given. Via specific examples, it is shown how the lattice Boltzmann (LB) method can be tuned to study phenomena as various as stability and dynamics of droplets on patterned substrates and collective behavior of suspensions of red blood cells under shear flow. While in these studies thermal fluctuations are ignored, they might be important in other cases such as colloidal dispersions and nano-droplets. For a study of this latter issue, we have recently proposed a theory in order to include thermal noise in lattice Boltzmann models for non-ideal fluids. We present main ideas of this theory and a test thereof in the case of spreading dynamics of nano-droplets on flat substrates. It is found that the well-known Tanner's law (which states that the droplet's base radius scales as R~t^1/10) is replaced by a faster spreading, R~t^1/6. This result is in agreement with previous works using scaling analysis of a stochastic lubrication equation. Fathollah Varnik, Interdisciplinary Centre for Advanced Materials Simulation (ICAMS) Ruhr University Bochum, Germany ---
“Phase-separation fronts in binary mixtures: lattice Boltzmann simulations and analytical solutions” When phase separation does occur in a sequential manner, e.g. due to the diffusion of a control parameter into the system, the resulting phase-separation structures have a markedly different appearance than homogeneous phase-separation patterns. The reason lies in the influence the already phase-separated material has on the newly phase-separating material. We call the region where phase-separation first occurs the phase-separation front. In this talk we will consider the simplest possible phase-separation front, i.e. a sharp transition in the control parameter moving through the system with a prescribed velocity inducing phase-separation. We show what structures are formed by such a front as a function of the front speed and the composition of the overtaken material. ---
“Lattice Boltzmann simulations of colloid-polymer mixtures” Colloid-polymer mixtures are proving a powerful model system to study molecular fluid-fluid interfaces[1]. Because of the ultralow interfacial tension many hydrodynamic phenomena take place much more slowly than in a normal fluid and can be observed directly in great detail, in both time and space, by combining confocal microscopy and microfluidics. Furthermore, due to the diffuse nature of the interface between the colloid-rich ‘liquid’ and the colloid-poor ‘gas’, multiphase lattice Boltzmann simulations provide the possibility of a quantitative comparison between simulation and experiment. We focus on the forced displacement of an interface between the liquid and gas phases in the gap between two parallel plates, and examine the resulting Saffmann-Taylor instability. Ioannis Zacharoudiou, Dirk Aarts and Julia Yeomans - The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK 1. D.G.A.L. Aarts, M. Schmidt, and H.N.W. Lekkerkerker, Direct visual observation of thermal capillary waves, Science 304, 847 (2004). [Back] |