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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…
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…