123 citations · 377 across the 39 of their papers we have counts for
31 papers · 1 filter
Discrete harmonics for stream function-vorticity Stokes problem
François Dubois, Michel Salaün, Stéphanie Salmon
We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite elements method of degree one converges…
Theory of the lattice Boltzmann method: discrete effects due to advection
Pierre Lallemand, François Dubois, Li-shi Luo
Lattice Boltzmann models are briefly introduced together with references to methods used to predict their ability for simulations of systems described by partial differential equat…
Conditions aux limites fortement non lin{é}aires pour les {é}quations d'Euler de la dynamique des gaz
François Dubois
We study various formulations of the boundary conditions for the Euler equations of gas dynamics from a mathematical and numerical point of view. In the case of one space dimension…
A variational symplectic scheme based on Simpson's quadrature
François Dubois, Juan Antonio Rojas-Quintero
We propose a variational symplectic numerical method for the time integration of dynamical systems issued from the least action principle. We assume a quadratic internal interpolat…
Numerical approximations of a lattice Boltzmann scheme with a family of partial differential equations
Bruce M Boghosian, François Dubois, Pierre Lallemand
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 in…
General fourth order Chapman-Enskog expansion of lattice Boltzmann schemes
François Dubois, Bruce M Boghosian, Pierre Lallemand
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 ma…
On single distribution lattice Boltzmann schemes for the approximation of Navier Stokes equations
François Dubois, Pierre Lallemand
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 wit…
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…
Generalized bounce back boundary condition for the nine velocities two-dimensional lattice Boltzmann scheme
François Dubois, Pierre Lallemand, Mohamed Mahdi Tekitek
In a previous work, we have proposed a method for the analysis of the bounce back boundary condition with the Taylor expansion method in the linear case. In this work two new schem…
Nonlinear fourth order Taylor expansion of lattice Boltzmann schemes
François Dubois
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 differ…
On anti bounce back boundary condition for lattice Boltzmann schemes
François Dubois, Pierre Lallemand, Mohamed-Mahdi Tekitek
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…
Equivalent partial differential equations of a lattice Boltzmann scheme
François Dubois
We show that when we formulate the lattice Boltzmann equation with a small time step t and an associated space scale x, a Taylor expansion joined with the so-called equivalen…
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…
Raviart Thomas Petrov-Galerkin Finite Elements
François Dubois, Isabelle Greff, Charles Pierre
The general theory of Babuška ensures necessary and sufficient conditions for a mixed problem in classical or Petrov-Galerkin form to be well posed in the sense of Hadamard. Moreov…
Raviart-Thomas finite elements of Petrov-Galerkin type
François Dubois, Isabelle Greff, Charles Pierre
The mixed finite element method for the Poisson problem with the Raviart-Thomas elements of low-level can be interpreted as a finite volume method with a non-local gradient. In thi…
Kron's method and cell complexes for magnetomotive and electromotive forces
Olivier Maurice, Alain Reineix, Philippe Durand +1
Starting from topological principles we first recall the elementary ones giving Kirchhoff's laws for current conservation. Using in a second step the properties of spaning tree, we…
On a superconvergent lattice Boltzmann boundary scheme
François Dubois, Pierre Lallemand, Mohamed Mahdi Tekitek
In a seminal paper Ginzburg and Adler analyzed the bounce-back boundary conditions for the lattice Boltzmann scheme and showed that it could be made exact to second order for the P…
On triangular lattice Boltzmann schemes for scalar problems
François Dubois, Pierre Lallemand
We propose to extend the d'Humiéres version of the lattice Boltzmann scheme to triangular meshes. We use Bravais lattices or more general lattices with the property that the degree…
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…
Comparison of Simulations of Convective Flows
Pierre Lallemand, François Dubois
We show that a single particle distribution for the D2Q13 lattice Boltzmann scheme can simulate coupled effects involving advection and diffusion of velocity and temperature. We co…
Some results on energy-conserving lattice Boltzmann models
Pierre Lallemand, François Dubois
We consider the problem of ''energy conserving'' lattice Boltzmann models. A major difficulty observed in previous studies is the coupling between the viscous and thermal waves eve…
Lorentz Transform and Staggered Finite Differences for Advective Acoustics
François Dubois, Eric Duceau, Frédéric Marechal +1
We study acoustic wave propagation in a uniform stationary flow. We develop a method founded on the Lorentz transform and a hypothesis of irrotationality of the acoustic perturbati…
An introduction to finite volumes for gas dynamics
François Dubois
We propose an elementary introduction to the finite volume method in the context of gas dynamics conservation laws. Our approach is founded on the advection equation, the exact int…