In the last two decades, the Lattice Boltzmann method (LBM) has emerged as a promising tool for modelling the Navier-Stokes equations and simulating complex fluid flows. LBM is based on microscopic models and mesoscopic kinetic equations. In some perspective, it can be viewed as a finite difference method for solving the Boltzmann transport equation. Moreover the Navier-Stokes equations can be ...

A new method for the computation of flows at the micrometer scale is presented. It is based on the recently introduced minimal entropic kinetic models. Both the thermal and isothermal families of minimal models are presented, and the simplest isothermal entropic lattice Bhatnagar-Gross-Krook (ELBGK) is studied in detail in order to quantify its relevance for microflow simulations. ELBGK is equi...

A lattice Boltzmann model for viscoelastic flow simulation is proposed. Elastic effects are taken into account within the framework of a Maxwell model. To test the approach, we estimate the transverse velocity autocorrelation function for a freely evolving system, and find clear manifestations of shear at large frequencies. We then characterize boundary-driven shear waves, and the resonant enha...

We present and analyze the Esoteric Twist algorithm for the Lattice Boltzmann Method. Esoteric Twist is a thread safe in-place streaming method that combines streaming and collision and requires only a single data set. Compared to other in-place streaming techniques, Esoteric Twist minimizes the memory footprint and the memory traffic when indirect addressing is used. Esoteric Twist is particul...

We develop a numerical framework for the quantum analogue of the “classical” lattice Boltzmann method (LBM), with the Maxwell-Boltzmann distribution replaced by the Fermi-Dirac function. To accommodate the spin density matrix, the distribution functions become 2× 2-matrix valued. We show that the efficient, commonly used BGK approximation of the collision operator is valid in the present settin...

We explore possible applications of the Lattice-Boltzmann Method for the simulation of geophysical flows. This fluid solver, while successful in other fields, is still rarely used for geotechnical applications. We show how the standard method can be modified to represent freesurface realization of mudflows, debris flows, and in general any plastic flow, through the implementation of a Bingham c...

For high-Reynolds number flows, the lattice Boltzmann method suffers from numerical instabilities that can induce local blowup of the computation. The von Neumann stability analysis applied to the LBE-BGK and LBE-MRT models shows that numerical instabilities occur in the high wavenumber range and are due to the interplay between acoustic modes and some other modes. As it is done in the LBE-MRT ...

An isothermal model on the standard two-dimension nine-velocity lattice (D2Q9) is proposed and analyzed. It originates from the thermal model with energy conservation introduced by N. I. Prasianakis and I. V. Karlin [Phys. Rev. E 76, 016702 (2007)]. The isothermal and the thermal equivalent models are tested through the simulation of the decay of a shear wave and of a temperature wave. Both are...

In this paper we shall briefly review a few Markov Chain Monte Carlo methods for simulating closed systems described by canonical ensembles. We cover both Boltzmann and non-Boltzmann sampling techniques. The Metropolis algorithm is a typical example of Boltzmann Monte Carlo method. We discuss the time-symmetry of the Markov chain generated by Metropolis like algorithms that obey detailed balanc...