A vectorial lattice Boltzmann scheme for the incompressible Navier-Stokes equations

Denise Aregba-Driollet; Thomas Bellotti; Roberto Natalini; Tommaso Tenna

A vectorial lattice Boltzmann scheme for the incompressible Navier-Stokes equations

Numerical Analysis 2026-07-27 v1 Fluid Dynamics

Authors: Denise Aregba-Driollet , Thomas Bellotti , Roberto Natalini , Tommaso Tenna

Abstract

We introduce a second-order accurate vectorial lattice Boltzmann scheme for the incompressible Navier-Stokes system, inspired by a discrete-velocity kinetic approximation proposed by Carfora and Natalini [ESAIM: M2AN, 42(1), 93-112, 2008]. Advantages and drawbacks compared to relaxation schemes are investigated by providing spectral analyses in the linearized case, and numerical validations on the genuinely non-linear problem.

Keywords

lattice boltzmann scheme incompressible navier-stokes vectorial scheme spectral analysis numerical validation

Cite

@article{arxiv.2607.24059,
  title  = {A vectorial lattice Boltzmann scheme for the incompressible Navier-Stokes equations},
  author = {Denise Aregba-Driollet and Thomas Bellotti and Roberto Natalini and Tommaso Tenna},
  journal= {arXiv preprint arXiv:2607.24059},
  year   = {2026}
}