A low-rank algorithm for weakly compressible flow
Numerical Analysis
2018-04-13 v1 Computational Physics
Abstract
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.
Keywords
Cite
@article{arxiv.1804.04561,
title = {A low-rank algorithm for weakly compressible flow},
author = {Lukas Einkemmer},
journal= {arXiv preprint arXiv:1804.04561},
year = {2018}
}