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

2026/07/27 by Denise Aregba-Driollet, Thomas Bellotti, Roberto Natalini +1
#math.NA #cs.NA #physics.flu-dyn

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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.

Citations

• Asymptotic preserving methods for the low mach limit in discrete velocity models approximating kinetic equations
• Equilibrium boundary conditions for vectorial multi-dimensional lattice Boltzmann schemes
• A positive- and bound-preserving vectorial lattice Boltzmann method in two dimensions
• Fourth-order entropy-stable lattice Boltzmann schemes for hyperbolic systems
• Simulation of strong nonlinear waves with vectorial lattice Boltzmann\n schemes
• Lattice BGK Models for Navier-Stokes Equation

Related

• Lattice Boltzmann inverse kinetic approach for the incompressible Navier-Stokes equations
• Increasing stability and accuracy of the lattice Boltzmann scheme: recursivity and regularization
• Kinetic multiscale scheme based on the discrete-velocity and lattice-Boltzmann methods
• Lattice Boltzmann schemes with relative velocities
• Asymptotic preserving methods for the low mach limit in discrete velocity models approximating kinetic equations