Droplet collision simulation by multi-speed lattice Boltzmann method

Realization of the Shan-Chen multiphase flow lattice Boltzmann model is considered in the framework of the higher-order Galilean invariant lattices. The present multiphase lattice Boltzmann model is used in two dimensional simulation of droplet collisions at high Weber numbers. Results are found to be in a good agreement with experimental findings

Lattice Boltzmann method for direct numerical simulation of turbulent flows

We present three-dimensional numerical simulations (DNS) of the Kida vortex flow, a prototypical turbulent flow, using a novel high-order lattice Boltzmann model. Extensive comparisons of various global and local statistical quantities obtained with an incompressible flow spectral element solver are reported. It is demonstrated that the lattice Boltzmann method is a promising alternative for DNS as it quantitatively capturesall the computed statistics of fluid turbulence

Dynamic mean-field models from a nonequilibrium thermodynamics perspective

Complicated dynamic models are often approximated by introducing mean-field approximations and closures. The focus here is on examining such mean-field models using nonequilibrium thermodynamics. Two illustrative examples are studied in terms of the double-generator general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework. First, it is shown that a model for the coil-stretch transition of long chains in strong elongation flows as proposed by de Gennes is thermodynamically admissible. In the second example, we study a Gaussian approximation, which is used to simplify the effect of hydrodynamic interactions in polymer solutions. This approximation, which is known to be in conflict with the fluctuation-dissipation theorem, is identified as defective directly when formulated in the thermodynamic formalism

On the Three-dimensional Central Moment Lattice Boltzmann Method

A three-dimensional (3D) lattice Boltzmann method based on central moments is derived. Two main elements are the local attractors in the collision term and the source terms representing the effect of external and/or self-consistent internal forces. For suitable choices of the orthogonal moment basis for the three-dimensional, twenty seven velocity (D3Q27), and, its subset, fifteen velocity (D3Q15) lattice models, attractors are expressed in terms of factorization of lower order moments as suggested in an earlier work; the corresponding source terms are specified to correctly influence lower order hydrodynamic fields, while avoiding aliasing effects for higher order moments. These are achieved by successively matching the corresponding continuous and discrete central moments at various orders, with the final expressions written in terms of raw moments via a transformation based on the binomial theorem. Furthermore, to alleviate the discrete effects with the source terms, they are treated to be temporally semi-implicit and second-order, with the implicitness subsequently removed by means of a transformation. As a result, the approach is frame-invariant by construction and its emergent dynamics describing fully 3D fluid motion in the presence of force fields is Galilean invariant. Numerical experiments for a set of benchmark problems demonstrate its accuracy.Comment: 55 pages, 8 figure

Nonintersecting Brownian motions on the half-line and discrete Gaussian orthogonal polynomials

We study the distribution of the maximal height of the outermost path in the model of $N$ nonintersecting Brownian motions on the half-line as $N\to \infty$, showing that it converges in the proper scaling to the Tracy-Widom distribution for the largest eigenvalue of the Gaussian orthogonal ensemble. This is as expected from the viewpoint that the maximal height of the outermost path converges to the maximum of the $\textrm{Airy}_2$ process minus a parabola. Our proof is based on Riemann-Hilbert analysis of a system of discrete orthogonal polynomials with a Gaussian weight in the double scaling limit as this system approaches saturation. We consequently compute the asymptotics of the free energy and the reproducing kernel of the corresponding discrete orthogonal polynomial ensemble in the critical scaling in which the density of particles approaches saturation. Both of these results can be viewed as dual to the case in which the mean density of eigenvalues in a random matrix model is vanishing at one point.Comment: 39 pages, 4 figures; The title has been changed from "The limiting distribution of the maximal height of nonintersecting Brownian excursions and discrete Gaussian orthogonal polynomials." This is a reflection of the fact that the analysis has been adapted to include nonintersecting Brownian motions with either reflecting of absorbing boundaries at zero. To appear in J. Stat. Phy

Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids

We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. We find the average domain size growing with time as $t^\gamma$, where $\gamma$ increases in the range $0.545 < \gamma < 0.717$, consistent with a crossover between diffusive $t^{1/3}$ and hydrodynamic viscous, $t^{1.0}$, behaviour. We find good collapse onto a single scaling function, yet the domain growth exponents differ from others' works' for similar values of the unique characteristic length and time that can be constructed out of the fluid's parameters. This rebuts claims of universality for the dynamical scaling hypothesis. At early times, we also find a crossover from $q^2$ to $q^4$ in the scaled structure function, which disappears when the dynamical scaling reasonably improves at later times. This excludes noise as the cause for a $q^2$ behaviour, as proposed by others. We also observe exponential temporal growth of the structure function during the initial stages of the dynamics and for wavenumbers less than a threshold value.Comment: 45 pages, 18 figures. Accepted for publication in Physical Review

Consequences of temperature fluctuations in observables measured in high energy collisions

We review the consequences of intrinsic, nonstatistical temperature fluctuations as seen in observables measured in high energy collisions. We do this from the point of view of nonextensive statistics and Tsallis distributions. Particular attention is paid to multiplicity fluctuations as a first consequence of temperature fluctuations, to the equivalence of temperature and volume fluctuations, to the generalized thermodynamic fluctuations relations allowing us to compare fluctuations observed in different parts of phase space, and to the problem of the relation between Tsallis entropy and Tsallis distributions. We also discuss the possible influence of conservation laws on these distributions and provide some examples of how one can get them without considering temperature fluctuations.Comment: Revised version of the invited contribution to The European Physical Journal A (Hadrons and Nuclei) topical issue about 'Relativistic Hydro- and Thermodynamics in Nuclear Physics' guest eds. Tamas S. Biro, Gergely G. Barnafoldi and Peter Va

Matrix lattice Boltzmann reloaded

The lattice Boltzmann equation has been introduced about twenty years ago as a new paradigm for computational fluid dynamics. In this paper, we revisit the main formulation of the lattice Boltzmann collision integral (matrix model) and introduce a new two-parametric family of collision operators which permits to combine enhanced stability and accuracy of matrix models with the outstanding simplicity of the most popular single-relaxation time schemes. The option of the revised lattice Boltzmann equation is demonstrated through numerical simulations of a three-dimensional lid driven cavity