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

  1. dynamical low-rank approximation
  2. projector splitting
  3. Boltzmann equation
  4. fluid dynamics
  5. weakly compressible flow

MSC codes

  1. 15A69
  2. 76M25
  3. 65M99

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Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A2795 - A2814
ISSN (online): 1095-7197

History

Submitted: 3 May 2018
Accepted: 9 July 2019
Published online: 10 September 2019

Keywords

  1. dynamical low-rank approximation
  2. projector splitting
  3. Boltzmann equation
  4. fluid dynamics
  5. weakly compressible flow

MSC codes

  1. 15A69
  2. 76M25
  3. 65M99

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