Related papers: Equivalent partial differential equations of a lat…
We systematically derived hydrodynamic equations and transport coefficients for a class of multi-speed lattice Boltzmann models in D dimensions, using the multi-scale technique. The constitutive relation of physical fluid is recovered by a…
In this contribution we extend the Taylor expansion method proposed previously by one of us and establish equivalent partial differential equations of DDH lattice Boltzmann scheme at an arbitrary order of accuracy. We derive formally the…
We derive a novel lattice Boltzmann scheme, which uses a pressure correction forcing term for approximating the volume averaged Navier-Stokes equations (VANSE) in up to three dimensions. With a new definition of the zeroth moment of the…
In this contribution we study the formal ability of a multi-resolution-times lattice Boltzmann scheme to approximate isothermal and thermal compressible Navier Stokes equations with a single particle distribution. More precisely, we…
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…
We determine properties of the lattice Boltzmann method for semiclassical fluids, which is based on the Boltzmann equation and the equilibrium distribution function is given either by the Bose-Einstein or the Fermi-Dirac ones. New…
Lattice Boltzmann models are briefly introduced together with references to methods used to predict their ability for simulations of systems described by partial differential equations that are first order in time and low order in space…
A numerical method, based on the discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged…
In this work, we study numerically the convergence of the scalar D2Q9 lattice Boltzmann scheme with multiple relaxation times when the time step is proportional to the space step and tends to zero. We do this by a combination of theory and…
We derive minimal discrete models of the Boltzmann equation consistent with equilibrium thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A simple analytical procedure of constructing the equilibrium for the…
In this contribution, we address the numerical solutions of high-order asymptotic equivalent partial differential equations with the results of a lattice Boltzmann scheme for an inhomogeneous advection problem in one spatial dimension. We…
We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultra-relativistic regime treated in the previous literature. Starting from an expansion of the…
We present a set of polynomial equations that provides models of the lattice Boltzmann theory for any required level of accuracy and for any dimensional space in a general form. We explicitly derive two- and three-dimensional models…
We propose a kinetic framework for single-component non-ideal isothermal flows. Starting from a kinetic model for a non-ideal fluid, we show that under conventional scaling the Navier-Stokes equations with a non-ideal equation of state are…
The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann methods is…
We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a…
We present a new kinetic model and its lattice Boltzmann realization for the simulation of compressible, non-ideal fluid flows. The method employs first-neighbour lattices and introduces a consistent set of correction terms constructed via…
We propose the derivation of acoustic-type isotropic partial differential equations that are equivalent to linear lattice Boltzmann schemes with a density scalar field and a momentum vector field as conserved moments. The corresponding…
It is well known that there are two integral steps of streaming and collision in the lattice Boltzmann method (LBM). This concept has been changed by the author's recently proposed macroscopic lattice Boltzmann method (MacLAB) to solve the…
The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the…