output
20102022
most citedProgramming Languages for Scientific Computing

158 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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15 papers · 1 filter

math.NA2022★ 5 cited

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…

math.NA2019★ 21 cited

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…

math.NA2018★ 123 cited

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…

math.NA2018★ 8 cited

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…

math.NA2018★ 4 cited

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…

math.NA2017

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…

math.NA2017

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…

math.NA2015★ 1 cited

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…

math.NA2014★ 29 cited

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…

math.NA2014★ 32 cited

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…

math.NA2014★ 1 cited

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…

math.NA2014★ 8 cited

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…

math.NA2013

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…

math.NA2013★ 10 cited

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…

math.NA2010★ 17 cited

Stable lattice Boltzmann schemes with a dual entropy approach for monodimensional nonlinear waves

François Dubois

We follow the mathematical framework proposed by Bouchut and present in this contribution a dual entropy approach for determining equilibrium states of a lattice Boltzmann scheme.…