Lattice Boltzmann method with self-consistent thermo-hydrodynamic equilibria

Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria, are placed within the framework of continuum kinetic theory. The mathematical treatment reveals that, in order to be consistent with the correct thermo-hydrodynamical description, temperature must also be shifted, besides momentum. New perspectives for the formulation of thermo-hydrodynamic lattice kinetic models of non-ideal fluids are then envisaged. It is also shown that on the lattice, the definition of the macroscopic temperature requires the inclusion of new terms directly related to discrete effects. The theoretical treatment is tested against a controlled case with a non ideal equation of state.Comment: 10 pages, 1 figur

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time $\tau$ and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation.Comment: 10 pages, no postscript figure provide

Three-Dimensional Multi-Relaxation Time (MRT) Lattice-Boltzmann Models for Multiphase Flow

In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show through the Chapman-Enskog multiscale analysis that the continuum limit behavior of 3D MRT LB models corresponds to that of the macroscopic dynamical equations for multiphase flow. We extend the 3D MRT LB models developed to represent multiphase flow with reduced compressibility effects. The multiphase models are evaluated by verifying the Laplace-Young relation for static drops and the frequency of oscillations of drops. The results show satisfactory agreement with available data and significant gains in numerical stability.Comment: Accepted for publication in the Journal of Computational Physic

Simulating Three-Dimensional Hydrodynamics on a Cellular-Automata Machine

We demonstrate how three-dimensional fluid flow simulations can be carried out on the Cellular Automata Machine 8 (CAM-8), a special-purpose computer for cellular-automata computations. The principal algorithmic innovation is the use of a lattice-gas model with a 16-bit collision operator that is specially adapted to the machine architecture. It is shown how the collision rules can be optimized to obtain a low viscosity of the fluid. Predictions of the viscosity based on a Boltzmann approximation agree well with measurements of the viscosity made on CAM-8. Several test simulations of flows in simple geometries -- channels, pipes, and a cubic array of spheres -- are carried out. Measurements of average flux in these geometries compare well with theoretical predictions.Comment: 19 pages, REVTeX and epsf macros require

Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media

Numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7.5 $\mu$m. One of the samples is a microtomographic image of Fontainebleau sandstone. Two of the samples are stochastic reconstructions with the same porosity, specific surface area, and two-point correlation function as the Fontainebleau sample. The fourth sample is a physical model which mimics the processes of sedimentation, compaction and diagenesis of Fontainebleau sandstone. The permeabilities of these samples are determined by numerically solving at low Reynolds numbers the appropriate Stokes equations in the pore spaces of the samples. The physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately, while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude. This finding confirms earlier qualitative predictions based on local porosity theory. Two numerical algorithms were used in these simulations. One is based on the lattice-Boltzmann method, and the other on conventional finite-difference techniques. The accuracy of these two methods is discussed and compared, also with experiment.Comment: to appear in: Phys.Rev.E (2002), 32 pages, Latex, 1 Figur

Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method

The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthes-Biesel, J. M. Rallison, The Time-Dependent Deformation of a Capsule Freely Suspended in a Linear Shear Flow, J. Fluid Mech. 113 (1981) 251-267]. Those analytic approximations are used to study the influence of the mesh tessellation method, the spatial resolution, and the discrete delta function of the immersed boundary method on the numerical results obtained by a coupled immersed boundary lattice Boltzmann finite element method. For the description of the capsule membrane, a finite element method and the Skalak constitutive model [R. Skalak et al., Strain Energy Function of Red Blood Cell Membranes, Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the investigation of the presented model for small resolutions to provide a sound basis for efficient but accurate simulations of multiple deformable particles immersed in a fluid. We come to the conclusion that details of the membrane mesh, as tessellation method and resolution, play only a minor role. The hydrodynamic resolution, i.e., the width of the discrete delta function, can significantly influence the accuracy of the simulations. The discretization of the delta function introduces an artificial length scale, which effectively changes the radius and the deformability of the capsule. We discuss possibilities of reducing the computing time of simulations of deformable objects immersed in a fluid while maintaining high accuracy.Comment: 23 pages, 14 figures, 3 table

Using the lid-driven cavity flow to validate moment-based boundary conditions for the Lattice Boltzmann Equation

The accuracy of the Moment Method for imposing no-slip boundary conditions in the lattice Boltzmann algorithm is investigated numerically using lid-driven cavity flow. Boundary conditions are imposed directly upon the hydrodynamic moments of the lattice Boltzmann equations, rather than the distribution functions, to ensure the constraints are satisfied precisely at grid points. Both single and multiple relaxation time models are applied. The results are in excellent agreement with data obtained from state-of-the-art numerical methods and are shown to converge with second order accuracy in grid spacing

Faits de société et nouvelles spatialités

[EN] New spatial devices appear when society changes. Today families are restructuring, the domestic group is recomposing, practices are evolving and housing should follow. How can it be transformed to adapt to the life conditions and the lifestyle desired by singles of any age, families -either monoparental or blended-, by the elderly? Experiences in many countries are described here, showing the diversity of the devices proposed and their underlying ideals. They range from a simple practical solution to live in a contemporary way, particularly because of the porosity between habitat and work, to the ambition to change life starting with housing. Built in several countries, they also have very different scales. A simple house shared by friends in Japan or Holland, they can also gather very large groups in Sweden or Switzerland. A long survey on cohabitation in France helps to feed the authors’ reflection.[FR] De nouveaux dispositifs spatiaux apparaissent quand la société change et aujourd’hui les familles se restructurent, le groupe domestique se recompose, les pratiques évoluent et le logement devrait suivre. Comment le transformer pour qu’il s’adapte aux conditions de vie et aux arts de vivre désirés par les célibataires de tous âges, les familles, qu’elles soient modales, mono-parentales ou recomposées, par les personnes âgées ? Des expériences tentées dans de nombreux pays sont relatées ici et montrent la diversité des dispositifs proposés et des idéaux qui les sous-tendent. Ils vont de la simple solution pratique pour vivre de façon contemporaine, notamment à cause de la porosité entre habitat et travail, à l’ambition de changer la vie en commençant par le logement. Construits dans plusieurs pays, ils ont aussi des échelles très différentes. Simple maison partagée par des amis au Japon ou en Hollande, ils peuvent aussi rassembler de très grands groupes en Suède ou en Suisse. Une longue enquête sur la cohabitation en France permet de nourrir la réflexion des auteursEleb, M.; Bendimérad, S. (2017). Facts of society and new spatialities. VLC arquitectura. Research Journal. 4(2):1-27. doi:10.4995/vlc.2017.7899SWORD12742Barthes, R. Comment vivre ensemble. Cours et séminaires au collège de France (1976-1977). Paris, Ed. du Seuil, 2002.Breviglieri, M. "Le temps des cohabitations ", in Habitat et vie urbaine. Changement dans les modes de vie, ed. Huynh, P.-M. Paris: Éditions du PUCA, 2006.Calliat, V. Parallèle des maisons de Paris construites depuis 1830 jusqu'à nos jours. Paris: Bance Ed., 1850.Didelon, V. "Kraftwerk, vers un nouvel âge de la coopération ", Criticat 11 (2013), 2-12.Dollé, N. "Quand seniors et étudiants cohabitent". In Habiter. Paris: Autrement, 2009.Eleb-Vidal, M. and Debarre-Blanchard, A. Architectures de la vie privée. Maisons et mentalités. XVIIe-XIXe siècles. Bruxelles: Édition Archives de l'Architecture Moderne, 1989.Eleb M., Châtelet, A.-M., Mandoul, T. Penser l'habiter. Le logement en questions. Liège, Paris: Éditions Mardaga, 1988.Eleb M. "L'habitat: flexible, adaptable, réversible?" In Villes, territoires, réversibilités, dir. Frank Scherrer, Martin Vanier. Paris: Ed. Hermann, 2013.Eleb M., Bendimérad, S. Vu de l'intérieur. Habiter un immeuble en Ile de France (1945-2010). Paris: Archibooks/Ordre des Architectes d'Ile de France, 2011.Eleb M., Simon, P. Entre confort, désirs et normes. Le logement contemporain (1995- 2010). Bruxelles: Editions Mardaga, 2013.Eleb M. Les 101 mots de l'habitat à l'usage de tous. Paris: Archibooks, 2015.Eleb M., Bendimérad, S. Ensemble mais séparément, des cohabitants et des lieux. Bruxelles: Mardaga, 2018.Ginzbourg M. Le style et l'époque. Problèmes de l'architecture moderne. Liège: Mardaga, 1986.Grisel J. and Bassand, N. "Typologie, participation et réversibilité ", Tracès 11 (2016), 12-16.Hayden, D. (1980). What Would a Non-Sexist City Be Like? Speculations on Housing, Urban Design, and Human Work. Signs: Journal of Women in Culture and Society, 5(S3), S170-S187. doi:10.1086/495718Horelli, L. "Self-Planned Housing and the reproduction of gender and identity". In Gender and the Built Environment, ed. L. Ottes, E. Poventud, M. van Schendelen & G. Segond von Banchet. Assen: Van Gorcum. 1995.Martial, A. (2003). S’apparenter. doi:10.4000/books.editionsmsh.575Martin E. "Voyage à Kraftwerk ", Criticat 11 (2013), 13-23.Nishizawa, Ryue. Workbook of Architecture. Tokyo: Heibonsha, 2013.Vestbro, Dirk Urban. "Saving by Sharing– Collective Housing for Sustainable Lifestyles in the Swedish Context", in 3rd International Conference on Degrowth for Ecological Sustainability and Social Equity, Venice, 19th – 23rd September 2012.Vestbro, D. U., & Horelli, L. (2012). Design for Gender Equality: The History of Co-Housing Ideas and Realities. Built Environment, 38(3), 315-335. doi:10.2148/benv.38.3.31