Kinetic derivation of a finite difference scheme for the incompressible Navier–Stokes equation

In the present paper the low Mach number limit of kinetic equations is used to develop a discretization for the incompressible Navier–Stokes equation. The kinetic equation is discretized with a first- and second-order discretization in space. The discretized equation is then considered in the low Mach number limit. Using this limit a second-order discretization for the convective part in the incompressible Navier–Stokes equation is obtained. Numerical experiments are shown comparing different approaches.