  In this paper, we propose a numerical method for solving weakly compressible
fluid flow based on a dynamical low-rank projector splitting. The low-rank
splitting scheme is applied to the Boltzmann equation with BGK collision term,
which results in a set of constant coefficient advection equations. This
procedure is numerically efficient as a small rank is sufficient to obtain the
relevant dynamics (described by the Navier--Stokes equations). The resulting
method can be combined with a range of different discretization strategies; in
particular, it is possible to implement spectral and semi-Lagrangian methods,
which allows us to design numerical schemes that are not encumbered by the
sonic CFL condition.
