50 citations · 136 across the 17 of their papers we have counts for
19 papers
Finite Difference formulation of any lattice Boltzmann scheme
Thomas Bellotti, Benjamin Graille, Marc Massot
Lattice Boltzmann schemes rely on the enlargement of the size of the target problem in order to solve PDEs in a highly parallelizable and efficient kinetic-like fashion, split into…
High accuracy analysis of adaptive multiresolution-based lattice Boltzmann schemes via the equivalent equations
Thomas Bellotti, Loïc Gouarin, Benjamin Graille +1
Multiresolution provides a fundamental tool based on the wavelet theory to build adaptive numerical schemes for Partial Differential Equations and time-adaptive meshes, allowing fo…
Does the multiresolution lattice Boltzmann method allow to deal with waves passing through mesh jumps?
Thomas Bellotti, Loïc Gouarin, Benjamin Graille +1
We consider an adaptive multiresolution-based lattice Boltzmann scheme, which we have recently introduced and studied from the perspective of the error control and the theory of th…
Multidimensional fully adaptive lattice Boltzmann methods with error control based on multiresolution analysis
Thomas Bellotti, Loïc Gouarin, Benjamin Graille +1
Lattice-Boltzmann methods are known for their simplicity, efficiency and ease of parallelization, usually relying on uniform Cartesian meshes with a strong bond between spatial and…
Multiresolution-based mesh adaptation and error control for lattice Boltzmann methods with applications to hyperbolic conservation laws
Loïc Gouarin, Benjamin Graille, Marc Massot +1
Lattice Boltzmann Methods (LBM) stand out for their simplicity and computational efficiency while offering the possibility of simulating complex phenomena. While they are optimal f…
Unexpected convergence of lattice Boltzmann schemes
Bruce Boghosian, François Dubois, Benjamin Graille +2
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 a…
A stability property for a mono-dimensional three velocities scheme with relative velocity
François Dubois, Benjamin Graille, S. V. Raghurama Rao
In this contribution, we study a stability notion for a fundamental linear one-dimensional lattice Boltzmann scheme, this notion being related to the maximum principle. We seek to…
A result of convergence for a mono-dimensional two-velocities lattice Boltzmann scheme
Filipa Caetano, François Dubois, Benjamin Graille
We consider a mono-dimensional two-velocities scheme used to approximate the solutions of a scalar hyperbolic conservative partial differential equation. We prove the convergence o…
Numerical treatment of the nonconservative product in a multiscale fluid model for plasmas in thermal nonequilibrium: application to solar physics
Quentin Wargnier, Sylvain Faure, Benjamin Graille +2
This contribution deals with the modeling of collisional multicomponent magnetized plasmas in thermal and chemical nonequilibrium aiming at simulating and predicting magnetic recon…
Curious convergence properties of lattice Boltzmann schemes for diffusion with acoustic scaling
Bruce Boghosian, François Dubois, Benjamin Graille +2
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…
Recovering the full Navier Stokes equations with lattice Boltzmann schemes
François Dubois, Benjamin Graille, Pierre Lallemand
We consider multi relaxation times lattice Boltzmann scheme with two particle distributions for the thermal Navier Stokes equations formulated with conservation of mass and momentu…
Stability of a bidimensional relative velocity lattice Boltzmann scheme
François Dubois, Tony Février, Benjamin Graille
In this contribution, we study the theoretical and numerical stability of a bidimensional relative velocity lattice Boltzmann scheme. These relative velocity schemes introduce a ve…
On the stability of a relative velocity lattice Boltzmann scheme for compressible Navier-Stokes equations
François Dubois, Tony Fevrier, Benjamin Graille
This paper studies the stability properties of a two dimensional relative velocity scheme for the Navier-Stokes equations. This scheme inspired by the cascaded scheme has the parti…
Third order equivalent equation for the relative velocity lattice Boltzmann schemes with one conservation law
Benjamin Graille, François Dubois, Tony Fevrier
We study the formal precision of the relative velocity lattice Boltzmann schemes. They differ from the d'Humières schemes by their relaxation phase: it occurs for a set of moments…
On rotational invariance of lattice Boltzmann schemes
Adeline Augier, François Dubois, Benjamin Graille +1
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 moment…
Lattice Boltzmann schemes with relative velocities
François Dubois, Tony Fevrier, Benjamin Graille
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…
Linear Lattice Boltzmann Schemes for Acoustic: parameters choices and isotropy properties
Adeline Augier, François Dubois, Benjamin Graille
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 pr…
Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9
Adeline Augier, François Dubois, Benjamin Graille
In this paper, we recall the linear version of the lattice Boltzmann schemes in the framework proposed by d'Humiéres. According to the equivalent equations we introduce a definitio…
Kinetic Theory of Plasmas: Translational Energy
Benjamin Graille, Thierry E. Magin, Marc Massot
In the present contribution, we derive from kinetic theory a unified fluid model for multicomponent plasmas by accounting for the electromagnetic field influence. We deal with a po…