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arXiv · 1804.04561

A low-rank algorithm for weakly compressible flow

Lukas Einkemmer
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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.

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Lukas Einkemmer. 2018-04-12. A low-rank algorithm for weakly compressible flow. https://arxiv.org/abs/1804.04561

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