Related papers: Gaussian Lattice Boltzmann method and its applicat…
Lattice Boltzmann method (LBM) is particularly well-suited for implementation on quantum circuits owing to its simple algebraic operations and natural parallelism. However, most quantum LBMs fix $\tau$ = 1 to avoid nonlinear collision,…
Derivation of the lattice Boltzmann method from the continuous kinetic theory [X. He and L. S. Luo, {\it Phys. Rev. E} {\bf 55}, R6333 (1997); X. Shan and X. He, {\it Phys. Rev. Lett.} {\bf 80}, 65 (1998)] is extended in order to obtain…
In this work, we consider a general consistent and conservative phase-field model for the incompressible two-phase flows. In this model, not only the Cahn-Hilliard or Allen-Cahn equation can be adopted, but also the mass and the momentum…
A detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method. Thorough comparisons with other numerical solutions for the two-dimensional, driven cavity flow show that the lattice Boltzmann method gives…
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…
The particles model, the collision model, the polynomial development used for the equilibrium distribution, the time discretization and the velocity discretization are factors that let the lattice Boltzmann framework (LBM) far away from its…
We develop a relativistic lattice Boltzmann (LB) model, providing a more accurate description of dissipative phenomena in relativistic hydrodynamics than previously available with existing LB schemes. The procedure applies to the…
The mass flow rate of Poiseuille flow of rarefied gas through long ducts of two-dimensional cross-sections with arbitrary shape are critical in the pore-network modeling of gas transport in porous media. In this paper, for the first time,…
In a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the Boltzmann type (G. Dimarco, R. Loubere, Towards an ultra efficient kinetic scheme. Part I: basics on the 689 BGK equation, J. Comp.…
In the paper we study the Boltzmann equation in the diffusive limit in a channel domain $\mathbb{T}^2\times (-1,1)$ for the 3D kinetic Couette flow. Our results demonstrate that the first-order approximation of the solutions is governed by…
We study efficient simulation of steady state for rarefied gas flow, which is modeled by the Boltzmann equation with BGK-type collision term. A nonlinear multigrid solver is proposed to resolve the efficiency issue by the following…
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…
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…
This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows. In contrast to other LBM for compressible flows, the vertices are organized in cells, and interpolation polynomials up to fourth…
We present here a comparison between collision-streaming and finite-difference lattice Boltzmann (LB) models. This study provides a derivation of useful formulae which help one to properly compare the simulation results obtained with both…
Ideal gases can be modeled by the Boltzmann equation from statistical physics. Instead of trying to track the position and velocity of a large number of gas molecules, it is possible to describe the particles with a particle distribution…
We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being…
We present a robust and accurate discretization approach for incompressible turbulent flows based on high-order discontinuous Galerkin methods. The DG discretization of the incompressible Navier-Stokes equations uses the local…
The discrete unified gas kinetic scheme (DUGKS) is a new finite volume (FV) scheme for continuum and rarefied flows which combines the benefits of both Lattice Boltzmann Method (LBM) and unified gas kinetic scheme (UGKS). By reconstruction…
We present a method to impose linear shear flow in discrete-velocity kinetic models of hydrodynamics through the use of sliding periodic boundary conditions. Our method is derived by an explicit coarse-graining of the Lees-Edwards boundary…