相关论文: On rotational invariance of lattice Boltzmann sche…
We propose a formal expansion of multiple relaxation times lattice Boltzmann schemes in terms of a single infinitesimal numerical variable. The result is a system of partial differential equations for the conserved moments of the lattice…
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…
Using the Taylor expansion method, we show that it is possible to improve the lattice Boltzmann method for acoustic applications. We derive a formal expansion of the eigenvalues of the discrete approximation and fit the parameters of the…
In order to derive the equivalent partial differential equations of a lattice Boltzmann scheme,the Chapman Enskog expansion is very popular in the lattive Boltzmann community. A maindrawback of this approach is the fact that multiscale…
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 paper, we investigate the numerous parameters choices for linear lattice Boltzmann schemes according to the definition of the isotropic order given in \cite{ADG11}. This property---written in a general framework including all of the…
Lattice Boltzmann methods are usually derived under the assumption of isotropy. In this work, we present a derivation of a Lattice Boltzmann method for anisotropic fluid flow. Starting from an anisotropic equilibrium distribution, we show a…
Lattice Boltzmann schemes are efficient numerical methods to solve a broad range of problems under the form of conservation laws. However, they suffer from a chronic lack of clear theoretical foundations. In particular, the consistency…
Lattice Boltzmann simulations of three-dimensional, isothermal hydrodynamics often use either the D3Q19 or the D3Q27 velocity sets. While both models correctly approximate Navier-Stokes in the continuum limit, the D3Q19 model is…
We consider multi relaxation times lattice Boltzmann scheme with two particle distributions for the thermal Navier Stokes equations formulated with conservation of mass and momentum and dissipation of volumic entropy.Linear stability is…
We propose a new macroscopic model derived from the classical nonlinear Boltzmann equation. A set of partial differential equations is obtained easily. The unknowns depend on the time and space coordinates, and are related to the…
We analyse a linear lattice Boltzmann (LB) formulation for simulation of linear acoustic wave propagation in heterogeneous media. We employ the single-relaxation-time Bhatnagar-Gross-Krook (BGK) as well as the general multi-relaxation-time…
In this paper, we recall the linear version of the lattice Boltzmann schemes in the framework proposed by d'Humi\'eres. According to the equivalent equations we introduce a definition for a scheme to be isotropic at some order. This…
We consider the D1Q3 lattice Boltzmann scheme with an acoustic scale for the simulation of diffusive processes. When the mesh is refined while holding the diffusivity constant, we first obtain asymptotic convergence. When the mesh size…
In this contribution, we recall the derivation of the anti bounce back boundary condition for the D2Q9 lattice Boltzmann scheme. We recall various elements of the state of the art for anti bounce back applied to linear heat and acoustics…
A general lattice Boltzmann (LB) model is proposed for solving nonlinear partial differential equations with the form $\partial_t \phi+\sum_{k=1}^{m} \alpha_k \partial_x^k \Pi_k (\phi)=0$, where $\alpha_k$ are constant coefficients, and…
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…
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, 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…
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…