22 citations · 30 across the 10 of their papers we have counts for
13 papers
On lattice Boltzmann scheme, finite volumes and boundary conditions
François Dubois, Pierre Lallemand
We develop the idea that a natural link between Boltzmann schemes and finite volumes exists naturally: the conserved mass and momentum during the collision phase of the Boltzmann s…
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…
Lattice Boltzmann model approximated with finite difference expressions
François Dubois, Pierre Lallemand, Christian Obrecht +1
We show that the asymptotic properties of the link-wise artificial compressibility method are not compatible with a correct approximation of fluid properties. We propose to adapt t…
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…
Coupling Linear Sloshing with Six Degrees of Freedom Rigid Body Dynamics
François Dubois, Dimitri Stoliaroff, Isabelle Terrasse
Fluid motion in tanks is usually described in space industry with the so-called Lomen hypothesis which assumes the vorticity is null in the moving frame. We establish in this contr…
Finite volumes and mixed Petrov-Galerkin finite elements : the unidimensional problem
François Dubois
For Laplace operator in one space dimension, we propose to formulate the heuristic finite volume method with the help of mixed Petrov-Galerkin finite elements. Weighting functions…
Simulation of strong nonlinear waves with vectorial lattice Boltzmann schemes
François Dubois
We show that an hyperbolic system with a mathematical entropy can be discretized with vectorial lattice Boltzmann schemes with the methodology of kinetic representation of the dual…
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…
On hyperbolic systems with entropy velocity covariant under the action of a group
François Dubois
For hyperbolic systems of conservation laws in one space dimension with a mathematical entropy, we define the notion of entropy velocity. Then we give sufficient conditions for suc…
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…