Benjamin Graille
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View article: A result of convergence for a mono-dimensional two-velocities lattice Boltzmann scheme
A result of convergence for a mono-dimensional two-velocities lattice Boltzmann scheme Open
We consider a mono-dimensional two-velocities scheme used to approximate the\nsolutions of a scalar hyperbolic conservative partial differential equation. We\nprove the convergence of the discrete solution toward the unique entropy\nsoluti…
View article: High accuracy analysis of adaptive multiresolution-based lattice Boltzmann schemes via the equivalent equations
High accuracy analysis of adaptive multiresolution-based lattice Boltzmann schemes via the equivalent equations Open
Multiresolution provides a fundamental tool based on the wavelet theory to build adaptive numerical schemes for Partial Differential Equations and time-adaptive meshes, allowing for error control. We have previously introduced this strateg…
View article: Multiresolution-Based Mesh Adaptation and Error Control for Lattice Boltzmann Methods with Applications to Hyperbolic Conservation Laws
Multiresolution-Based Mesh Adaptation and Error Control for Lattice Boltzmann Methods with Applications to Hyperbolic Conservation Laws Open
Lattice Boltzmann Methods (LBM) stand out for their simplicity and\ncomputational efficiency while offering the possibility of simulating complex\nphenomena. While they are optimal for Cartesian meshes, adapted meshes have\ntraditionally b…
View article: Does the multiresolution lattice Boltzmann method allow to deal with waves passing through mesh jumps?
Does the multiresolution lattice Boltzmann method allow to deal with waves passing through mesh jumps? Open
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 the equivalent equations. This numerical strategy leads to hi…
View article: High accuracy analysis of adaptive multiresolution-based lattice Boltzmann schemes via the equivalent equations
High accuracy analysis of adaptive multiresolution-based lattice Boltzmann schemes via the equivalent equations Open
Multiresolution provides a fundamental tool based on the wavelet theory to build adaptive numerical schemes for Partial Differential Equations and time-adaptive meshes, allowing for error control. We have introduced this strategy before to…
View article: Does the multiresolution lattice Boltzmann method allow to deal with waves passing through mesh jumps?
Does the multiresolution lattice Boltzmann method allow to deal with waves passing through mesh jumps? Open
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 the equivalent equations. This numerical strategy leads to hi…
View article: Multidimensional fully adaptive lattice Boltzmann methods with error control based on multiresolution analysis
Multidimensional fully adaptive lattice Boltzmann methods with error control based on multiresolution analysis Open
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 temporal discretization. This fact complicates the crucial…
View article: Multiresolution-based mesh adaptation and error control for lattice Boltzmann methods with applications to hyperbolic conservation laws
Multiresolution-based mesh adaptation and error control for lattice Boltzmann methods with applications to hyperbolic conservation laws Open
Lattice Boltzmann Methods (LBM) stand out for their simplicity and computational efficiency while offering the possibility of simulating complex phenomena. While they are optimal for Cartesian meshes, adapted meshes have traditionally been…
View article: Unexpected convergence of lattice Boltzmann schemes
Unexpected convergence of lattice Boltzmann schemes Open
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 and tends to zero. We do this by a combination of theory and…
View article: A stability property for a mono-dimensional three velocities scheme with relative velocity
A stability property for a mono-dimensional three velocities scheme with relative velocity Open
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 characterize the parameters of the scheme that guarantee th…
View article: A result of convergence for a mono-dimensional two-velocities lattice Boltzmann scheme
A result of convergence for a mono-dimensional two-velocities lattice Boltzmann scheme Open
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 of the discrete solution toward the unique entropy solution …
View article: Multicomponent fluid model for two-temperature plasmas derived from kinetic theory : application to magnetic reconnection
Multicomponent fluid model for two-temperature plasmas derived from kinetic theory : application to magnetic reconnection Open
This contribution deals with the fluid modeling of multicomponent magnetized plasmas in thermo-chemical non-equilibrium from the partially- to fully-ionized collisional regimes, aiming at the predictive simulation of magnetic reconnection …
View article: Curious Convergence Properties of Lattice Boltzmann Schemes for Diffusion with Acoustic Scaling
Curious Convergence Properties of Lattice Boltzmann Schemes for Diffusion with Acoustic Scaling Open
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 first obtain asymptotic convergence. When the mesh size ten…
View article: Recovering the full Navier Stokes equations with lattice Boltzmann schemes
Recovering the full Navier Stokes equations with lattice Boltzmann schemes Open
We consider multi relaxation times lattice Boltzmann scheme with two particle\ndistributions for the thermal Navier Stokes equations formulated with\nconservation of mass and momentum and dissipation of volumic entropy.Linear\nstability is…
View article: Stability of a bidimensional relative velocity lattice Boltzmann scheme
Stability of a bidimensional relative velocity lattice Boltzmann scheme Open
In this contribution, we study the theoretical and numerical stability of a bidimensional relative velocity lattice Boltzmann scheme. These relative velocity schemes introduce a velocity field parameter called "relative velocity" function …
View article: Lattice Boltzmann Schemes with Relative Velocities
Lattice Boltzmann Schemes with Relative Velocities Open
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 method of d’Humières. They extend also the Geier’s cascaded…
View article: On the stability of a relative velocity lattice Boltzmann scheme for compressible Navier-Stokes equations
On the stability of a relative velocity lattice Boltzmann scheme for compressible Navier-Stokes equations Open
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 particularity to relax in a frame moving with a velocity field f…
View article: On the stability of a relative velocity lattice Boltzmann scheme for\n compressible Navier-Stokes equations
On the stability of a relative velocity lattice Boltzmann scheme for\n compressible Navier-Stokes equations Open
This paper studies the stability properties of a two dimensional relative\nvelocity scheme for the Navier-Stokes equations. This scheme inspired by the\ncascaded scheme has the particularity to relax in a frame moving with a\nvelocity fiel…
View article: Third order equivalent equation for the relative velocity lattice Boltzmann schemes with one conservation law
Third order equivalent equation for the relative velocity lattice Boltzmann schemes with one conservation law Open
We study the formal precision of the relative velocity lattice Boltzmann schemes. They differ from the d'Humi\`eres schemes by their relaxation phase: it occurs for a set of moments parametrized by a velocity field function of space and ti…
View article: Third order equivalent equation for the relative velocity lattice Boltzmann schemes with one conservation law
Third order equivalent equation for the relative velocity lattice Boltzmann schemes with one conservation law Open
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 parametrized by a velocity field function of space and time…