Related papers: Fully dissipative relativistic lattice Boltzmann m…
We introduce a new method of statistical analysis to characterise the dynamics of turbulent fluids in two dimensions. We establish that, in equilibrium, the vortex distributions can be uniquely connected to the temperature of the vortex…
In this paper, the performance of two lattice Boltzmann method formulations for yield-stress (i.e. viscoplastic) fluids has been investigated. The first approach is based on the popular Papanastasiou regularisation of the fluid rheology in…
Finite-difference Lattice Boltzmann (LB) models are proposed for simulating gas flows in devices with microscale geometries. The models employ the roots of half-range Gauss-Hermite polynomials as discrete velocities. Unlike the standard LB…
In spite of the large number of papers appeared in the past which are devoted to the lattice Boltzmann (LB) methods, basic aspects of the theory still remain unchallenged. An unsolved theoretical issue is related to the construction of a…
We derive the transport coefficients of second-order fluid dynamics with $14$ dynamical moments using the method of moments and the Chapman-Enskog method in the relaxation-time approximation for the collision integral of the relativistic…
In this contribution, a new class of lattice Boltzmann schemes is introduced and studied. These schemes are presented in a framework that generalizes the multiple relaxation times method of d'Humi\`eres. They extend also the Geier's…
The complete set of transport coefficients for two dimensional relativistic degenerate gases is derived within a relaxation approximation in kinetic theory, by considering both the particle and energy frames. A thorough comparison between…
We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Boltzmann equations. The equations are discretized with Hermite polynomials in velocity space yielding a first order…
The Lattice Boltzmann Method (LBM) has emerged as a powerful tool in computational fluid dynamics and material science. However, standard LBM formulation imposes some limitations on the applications of the method, particularly compressible…
Generalizing the collision term in the relativistic Boltzmann equation to include nonlocal effects, and using Grad's 14-moment approximation for the single-particle distribution function, we derive evolution equations for the relativistic…
A new lattice Boltzmann method for simulating multiphase flows is developed theoretically. The method is adjusted such that its continuum limit is the Navier-Stokes equation, with a driving force derived from the Cahn-Hilliard free energy.…
The recently introduced consistent lattice Boltzmann model with energy conservation [S. Ansumali, I.V. Karlin, Phys. Rev. Lett. 95, 260605 (2005)] is extended to the simulation of thermal flows on standard lattices. The two-dimensional…
In this paper, we investigate the recently developed lattice Boltzmann model for relativistic hydrodynamics. To this purpose, we perform simulations of shock waves in quark-gluon plasma in the low and high viscosities regime, using three…
We develop our recently proposed lattice-Boltzmann method for the non-equilibrium dynamics of amphiphilic fluids (Chen, Boghosian, Coveney and Nekovee, Proc. Roy. Soc. London A, 456, 1431 (2000).) Our method maintains an orientational…
Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann (LB) model that describes a two-dimensional ($2D$) fluid obeying the van der Waals equation of state, is introduced.…
Lattice Boltzmann model for viscoelastic flow simulation is proposed; elastic effects are taken into account in the framework of Maxwell model. The following three examples are studied using the proposed approach: a transverse velocity…
The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response…
We present a construction of a (d+2)-dimensional Ricci-flat metric corresponding to a (d+1)-dimensional relativistic fluid, representing holographically the hydrodynamic regime of a (putative) dual theory. We show how to obtain the metric…
In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard D2Q9 lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and…
A Lattice Boltzmann formulation for relativistic fluids is presented and numerically verified through quantitative comparison with recent hydrodynamic simulations of relativistic shock-wave propagation in viscous quark-gluon plasmas. This…