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

René Beltman; Martijn Anthonissen; Barry Koren

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

René Beltman, Martijn Anthonissen, Barry Koren

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

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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 language	English
Title of host publication	Proceedings of the 6th European Conference on Computational Mechanics
Subtitle of host publication	Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
Editors	Roger Owen, Rene de Borst, Jason Reese, Chris Pearce
Publisher	International Center for Numerical Methods in Engineering (CIMNE)
Pages	4087-4098
Number of pages	12
ISBN (Electronic)	9788494731167
Publication status	Published - 2020
Event	6th 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 2018 → 15 Jun 2018

Conference

Conference	6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018
Country/Territory	United Kingdom
City	Glasgow
Period	11/06/18 → 15/06/18

Keywords

Cartesian mesh
Conservative
Cut-cell method
Mimetic
Navier-Stokes

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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).

Beltman, René ; Anthonissen, Martijn ; Koren, Barry. / A locally refined cut-cell method with exact conservation for the incompressible Navier-Stokes equations. 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. editor / Roger Owen ; Rene de Borst ; Jason Reese ; Chris Pearce. International Center for Numerical Methods in Engineering (CIMNE), 2020. pp. 4087-4098

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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.",

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booktitle = "Proceedings of the 6th European Conference on Computational Mechanics",

publisher = "International Center for Numerical Methods in Engineering (CIMNE)",

note = "6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 ; Conference date: 11-06-2018 Through 15-06-2018",

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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. International Center for Numerical Methods in Engineering (CIMNE), pp. 4087-4098, 6th 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, 11/06/18.

A locally refined cut-cell method with exact conservation for the incompressible Navier-Stokes equations. / Beltman, René ; Anthonissen, Martijn ; Koren, Barry.
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. ed. / Roger Owen; Rene de Borst; Jason Reese; Chris Pearce. International Center for Numerical Methods in Engineering (CIMNE), 2020. p. 4087-4098.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T1 - A locally refined cut-cell method with exact conservation for the incompressible Navier-Stokes equations

AU - Beltman, René

AU - Anthonissen, Martijn

AU - Koren, Barry

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Cartesian mesh

KW - Conservative

KW - Cut-cell method

KW - Mimetic

KW - Navier-Stokes

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EP - 4098

BT - Proceedings of the 6th European Conference on Computational Mechanics

A2 - Owen, Roger

A2 - de Borst, Rene

A2 - Reese, Jason

A2 - Pearce, Chris

PB - International Center for Numerical Methods in Engineering (CIMNE)

T2 - 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018

Y2 - 11 June 2018 through 15 June 2018

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Beltman R , Anthonissen M , Koren B. A locally refined cut-cell method with exact conservation for the incompressible Navier-Stokes equations. In Owen R, de Borst R, Reese J, Pearce C, editors, 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. International Center for Numerical Methods in Engineering (CIMNE). 2020. p. 4087-4098

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

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