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

Particle-laden two-dimensional elastic turbulence

The aggregation properties of heavy inertial particles in the elastic turbulence regime of an Oldroyd-B fluid with periodic Kolmogorov mean flow are investigated by means of extensive numerical simulations in two dimensions. Both the small and large scale features of the resulting inhomogeneous particle distribution are examined, focusing on their connection with the properties of the advecting viscoelastic flow. We find that particles preferentially accumulate on thin highly elastic propagating waves and that this effect is largest for intermediate values of particle inertia. We provide a quantitative characterization of this phenomenon that allows to relate it to the accumulation of particles in filamentary highly strained flow regions producing clusters of correlation dimension close to 1. At larger scales, particles are found to undergo turbophoretic-like segregation. Indeed, our results indicate a close relationship between the profiles of particle density and fluid velocity fluctuations. The large-scale inhomogeneity of the particle distribution is interpreted in the framework of a model derived in the limit of small, but finite, particle inertia. The qualitative characteristics of different observables are, to a good extent, independent of the flow elasticity. When increased, the latter is found, however, to slightly reduce the globally averaged degree of turbophoretic unmixing.Comment: 12 pages, 9 figures. Submitted to EPJ

Étude numérique de l'effet de l'élasticité sur la vitesse axiale et les vortex dans un écoulement d'un fluide viscoélastique à faibles nombres de Dean dans une conduite courbe

Le travail présenté porte sur les vortex de Dean qui s’opèrent dans les conduites courbes. Les simulations numériques sont faites pour un fluide de Phan-Thien-Tanner et un fluide newtonien s’écoulant à des faibles nombres de Reynolds (Re) dans une conduite courbe à section carrée. Le nombre de Deborah (De) varie de 0 à 0,6. La méthode des volumes finis avec un maillage décalé est utilisée pour résoudre les équations de conservation de masse et de quantité de mouvement et l’équation constitutive de Phan-Thien-Tanner (PTT) représentant le fluide viscoélastique. Les équations sont écrites en utilisant les coordonnées orthogonales généralisées qui sont mieux adaptées pour les écoulements présentant des courbures significatives. Les résultats obtenus mettent en évidence l’influence de la viscoélasticité sur la formation et la structure des vortex de Dean ainsi que le champ dynamique de l’écoulement et en particuliers la vitesse axiale de l’écoulement principal

Etude numérique des Vortex de Dean dans un écoulement d'un fluide viscoélastique dans une conduite courbe

Le présent travail est une synthèse de simulations numériques des écoulements de fluides viscoélastiques par la méthode des volumes finis. Pour étudier l'effet de l'élasticité sur les vortex de Dean le nombre de Deborah est varié de 0.1 à 0.5, l'effet de la géométrie est étudié en variant le taux de courbure de 2.5 à 20 et le rapport d'aspect de 1 à 12. Les résultats obtenus mettent en évidence l'influence des paramètres rhéologiques et des paramètres géométriques sur les conditions d'apparition et la structure des vortex de Dean

An objective perspective for classic flow classification criteria

Four classic criteria used to the classification of complex flows are discussed here. These criteria are useful to identify regions of the flow related to shear, elongation or rigid-body motion. These usual criteria, namely $Q$, $\Delta$, $\lambda_{2}$ and $\lambda_{cr}/\lambda_{ci}$, use the fluid's rate-of-rotation tensor, which is known to vary with respect to a reference frame. The advantages of using objective (invariant with respect to a general transformation on the reference frame) criteria are discussed in the present work. In this connection, we construct versions of classic criteria replacing standard vorticity, a non-objective quantity, by effective vorticity, a rate of rotation tensor with respect to the angular velocity of the eigenvectors of the strain rate tensor. The classic criteria and their corresponding objective versions are applied to classify two complex flows: the transient ABC flow and the flow through the abrupt 4:1 contraction. It is shown that the objective versions of the criteria provide richer information on the kinematics of the flowComment: 11 pages, 4 figures (minor corrections and improvements

Surface light modulation by sea ice and phytoplankton survival in a convective flow model

Plankton dynamics depend in a complex manner on a variety of physical phenomena, according to both experimental and numerical data. In particular, experimental field studies have highlighted the relation between phytoplankton survival and turbulent upwelling and downwelling from thermal convection. Recent numerical works have also shown the importance of accounting for advective transport by persistent structures in simulation models. In nutrient-rich polar marine environments phytoplankton blooms are critically limited by light availability under ice-covered waters. Such heterogeneity of the light intensity distribution, in association with a large-scale coherent fluid flow, can give rise to nontrivial growth dynamics. In this work we extend a previous advection-reaction-diffusion model of phytoplankton light-limited vertical dynamics in the presence of convective transport. Specifically, we consider horizontally heterogeneous light conditions through the use of two regions with different production regimes, modelling the absence (presence) of light under (in between) obstacles. Such a model is intended as an idealized representation of nonuniformly ice-covered polar waters. By means of numerical simulations, we find that the main role of advective transport is to hinder phytoplankton growth, but also that such effect depends on the positions of the obstacles with respect to the upwelling and downwelling flow regions. Furthermore, we show that the sinking speed due to the density difference between phytoplankton organisms and water, while small, plays an important role, which depends on how it adds to the flow. These results indicate that advective transport can have a crucial impact on the survival conditions of sinking phytoplankton species in polar environments.Comment: 10 pages, 5 figure

Simulation numérique des écoulements Newtonien et viscoélastique dans une conduite courbe de 180 degrés avec section carrée

Ce travail présente les résultats numériques et une analyse des fluides Newtonien et viscoélastique du type Phan-Thien-Tanner (PTT), dans une conduite courbe de 180° avec section carrée. Les équations de Navier Stokes sont écrites en coordonnées orthogonales généralisées, et résolues en utilisant la méthode des volumes finis. On montre les résultats numériques pour nombres de Dean (125, 137, 150), ainsi que les profils de vitesses, lignes de courant, vortex dans la zone courbée et la région de sortie. Une étude sur influence de la longueur dans la zone de sortie est réalisée

Étude numérique de l'effet de la portance inverse pour un fluide de Bingham autour d'un obstacle

Ce travail porte sur la simulation numérique d'un écoulement de fluide non-Newtonien (Bingham) autour d'un obstacle en forme de profil hydrodynamique. La méthode des volumes finis avec un maillage orthogonale généralisée est utilisée. Les résultats du calcul montrent une portance inverse pour l'écoulement du fluide de Bingham en régime laminaire. Ceci est en accord avec des résultats expérimentaux concernant la portance inverse obtenus par B. Dollet et al. (Physical Review Letters, 2005) pour une solution mousseuse

Development of secondary flows in viscoelastic curved ducts and the influence of outlet region

International audienceThis paper presents numerical simulations of Newtonian and viscoelastic flows through a 180° curved duct of square cross section with a long straight outlet region. A particular attention is paid to the development of the flow in the output rectangular region after the curved part. The viscoelastic fluid is modeled using the constitutive equation proposed by Phan-Thien-Tanner (PTT). The numerical results, obtained with a finite-volume method, are shown for three different Dean numbers (125,137,150)(125,137,150) and for three Deborah numbers (0.1,0.2,0.3)(0.1,0.2,0.3). The necessary outlet length to impose boundary conditions is presented and discussed for these cases. Streamlines and vortex formation are shown to illustrate and analyze the evolution of the secondary flow in this region