A locally refined cut-cell method with exact conservation for the incompressible Navier-Stokes equations

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Abstract

We present a mimetic discretization of the incompressible Navier-Stokes equations for general polygonal meshes. The discretization employs staggered velocity variables and results in discrete equations that exactly conserve mass, momentum and kinetic energy (in the inviscid limit) up to and including the boundaries where Dirichlet conditions apply. Moreover, the discrete equations give rise to a discrete global vorticity that is consistent with the Dirichlet boundary conditions. As the method retains all its favorable properties on general meshes, it can be perfectly applied as a locally refined Cartesian mesh cut-cell method. We numerically verify the conservation properties for the lid-driven cavity flow and demonstrate the method for the unsteady flow around a circular cylinder.

Original languageEnglish
Title of host publicationProceedings of the 6th European Conference on Computational Mechanics
Subtitle of host publicationSolids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
EditorsRoger Owen, Rene de Borst, Jason Reese, Chris Pearce
PublisherInternational Center for Numerical Methods in Engineering (CIMNE)
Pages4087-4098
Number of pages12
ISBN (Electronic)9788494731167
Publication statusPublished - 2020
Event6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 - Glasgow, United Kingdom
Duration: 11 Jun 201815 Jun 2018

Conference

Conference6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018
CountryUnited Kingdom
CityGlasgow
Period11/06/1815/06/18

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Keywords

  • Cartesian mesh
  • Conservative
  • Cut-cell method
  • Mimetic
  • Navier-Stokes

Cite this

Beltman, R., Anthonissen, M., & Koren, B. (2020). A locally refined cut-cell method with exact conservation for the incompressible Navier-Stokes equations. In R. Owen, R. de Borst, J. Reese, & C. Pearce (Eds.), Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 (pp. 4087-4098). International Center for Numerical Methods in Engineering (CIMNE).