A fully conservative mimetic discretization of the Navier–Stokes equations in cylindrical coordinates with associated singularity treatment

Guido Oud, Duncan van der Heul, Kees Vuik, Ruud Henkes

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

We present a finite difference discretization of the incompressible Navier–Stokes equations in cylindrical coordinates. This currently is, to the authors' knowledge, the only scheme available that is demonstrably capable of conserving mass, momentum and kinetic energy (in the absence of viscosity) on both uniform and non-uniform grids. Simultaneously, we treat the inherent discretization issues that arise due to the presence of the coordinate singularity at the polar axis. We demonstrate the validity of the conservation claims by performing a number of numerical experiments with the proposed scheme, and we show that it is second order accurate in space using the Method of Manufactured Solutions.
Original languageEnglish
Pages (from-to)314-337
Number of pages24
JournalJournal of Computational Physics
Volume325
DOIs
Publication statusPublished - 2016

Keywords

  • Incompressible flow
  • Cylindrical coordinates
  • Mimetic finite difference method
  • Kinetic energy conservation

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