A low-rank algorithm for weakly compressible flow
This work addresses the computational bottleneck of simulating weakly compressible flows for researchers in computational fluid dynamics, offering a method that can be combined with spectral or semi-Lagrangian discretizations to overcome time-step restrictions.
The paper proposes a low-rank numerical method for weakly compressible flow by applying a dynamical low-rank projector splitting to the Boltzmann equation with BGK collision term, achieving efficiency by using a small rank to capture Navier-Stokes dynamics and avoiding the sonic CFL condition.
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.