44 citations · 83 across the 13 of their papers we have counts for
17 papers
A vectorial lattice Boltzmann scheme for the incompressible Navier-Stokes equations
Denise Aregba-Driollet, Thomas Bellotti, Roberto Natalini +1
We introduce a second-order accurate vectorial lattice Boltzmann scheme for the incompressible Navier-Stokes system, inspired by a discrete-velocity kinetic approximation proposed…
Convergence of a two-relaxation-times kinetic approximation towards the solution of a scalar conservation law
Denise Aregba-Driollet, Thomas Bellotti
We introduce a two-relaxation-times (TRT) kinetic approximation for scalar non-linear conservation laws in one space dimension, addressing the convergence of relaxation approximati…
Long-time behavior of multi-step Finite Difference schemes with boundary via steepest descent and analytic combinatorics
Thomas Bellotti, Tommaso Tenna
We demonstrate how steepest descent arguments and singularity analysis from analytic combinatorics allow for an accurate description of the behavior of linear numerical schemes --…
Perfectly transparent boundary conditions and wave propagation in lattice Boltzmann schemes
Thomas Bellotti
Systems of N = 1, 2, . . . first-order hyperbolic conservation laws feature N undamped waves propagating at finite speeds. On their own hand, multi-step Finite Difference and latti…
Stability of lattice Boltzmann schemes for initial boundary value problems in raw formulation
Thomas Bellotti
We study the stability of one-dimensional linear lattice Boltzmann schemes for scalar hyperbolic equations with respect to boundary data. Our approach is based on the original raw…
Equilibrium boundary conditions for vectorial multi-dimensional lattice Boltzmann schemes
Denise Aregba-Driollet, Thomas Bellotti
The concept of equilibrium is a general tool to fill the gap between macroscopic and mesoscopic information, both within kinetic systems and kinetic schemes. This work explores the…
Monotonicity and convergence of two-relaxation-times lattice Boltzmann schemes for a non-linear conservation law
Denise Aregba-Driollet, Thomas Bellotti
We address the convergence analysis of lattice Boltzmann methods for scalar non-linear conservation laws, focusing on two-relaxation-times (TRT) schemes. Unlike Finite Difference/F…
Consistency and stability of boundary conditions for a two-velocities lattice Boltzmann scheme
Thomas Bellotti
We theoretically explore boundary conditions for lattice Boltzmann methods, focusing on a toy two-velocities scheme to tackle a linear one-dimensional advection equation. By mappin…
Fourth-order entropy-stable lattice Boltzmann schemes for hyperbolic systems
Thomas Bellotti, Philippe Helluy, Laurent Navoret
We present a novel framework for the development of fourth-order lattice Boltzmann schemes to tackle multidimensional nonlinear systems of conservation laws. As for other numerical…
The influence of parasitic modes on "weakly'' unstable multi-step Finite Difference schemes
Thomas Bellotti
Numerical analysis for linear constant-coefficients Finite Difference schemes was developed approximately fifty years ago. It relies on the assumption of scheme stability and in pa…
Initialisation from lattice Boltzmann to multi-step Finite Difference methods: modified equations and discrete observability
Thomas Bellotti
Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can…
Truncation errors and modified equations for the lattice Boltzmann method via the corresponding Finite Difference schemes
Thomas Bellotti
Lattice Boltzmann schemes are efficient numerical methods to solve a broad range of problems under the form of conservation laws. However, they suffer from a chronic lack of clear…
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…