123 citations · 377 across the 39 of their papers we have counts for
43 papers
Isotropy and Galilean invariance of Lattice Boltzmann Method: Theoretical and numerical analysis using oblique dipole benchmark *
François Dubois, Souleymane Kadri Harouna, Pierre Lallemand +1
This work focuses on the two-dimensional, nine-velocity (D2Q9) lattice Boltzmann model. First, we show that the D2Q9 scheme cannot achieve secondorder accuracy unless the cubic vel…
A lattice Boltzmann scheme with equilateral triangles for diffusion and acoustics
Francois Dubois, Pierre Lallemand
This contribution studies the Boltzmann scheme on a ``D2T4''grid constructed on meshes using equilateral triangles. The center of each triangle is connected to itself and to three…
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…
On Macroscopic Intricate States
François Dubois
The present contribution is in the field of quantum modelling of macroscopic phenomena. The focus is on one enigmatic aspect of quantum physics, namely the Einstein-Podolsky-Rosen…
On quantum models for opinion and voting intention polls
François Dubois
In this contribution, we construct a connection between two quantum voting models presented previously. We propose to try to determine the result of a vote from associated given op…
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…
On Voting Process and Quantum Mechanics
François Dubois
In this communication, we propose a tentative to set the fundamental problem of measuring process done by a large structure on a microsopic one. We consider the example of voting w…
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…
Pontryagin calculus in Riemannian geometry
François Dubois, Danielle Fortuné, Juan Antonio Rojas Quintero +1
In this contribution, we study systems with a finite number of degrees of freedom as in robotics. A key idea is to consider the mass tensor associated to the kinetic energy as a me…
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…
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…
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…
Eigenlogic: Interpretable Quantum Observables with applications to Fuzzy Behavior of Vehicular Robots
Zeno Toffano, François Dubois
This work proposes a formulation of propositional logic, named Eigenlogic, using quantum observables as propositions. The eigenvalues of these operators are the truth-values and th…