Conservative mimetic cut-cell method for incompressible Navier-Stokes equations

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Abstract

We introduce a mimetic Cartesian cut-cell method for incompressible viscous flow that conserves mass, momentum, and kinetic energy in the inviscid limit, and determines the vorticity such that the global vorticity is consistent with the boundary conditions. In particular we discuss how the no-slip boundary conditions should be applied in a conservative way on objects immersed in the Cartesian mesh. We use the method to compute the flow around a cylinder. We find a good comparison between our results and benchmark results for both a steady and an unsteady test case.

Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications ENUMATH 2017
EditorsFlorin Adrian Radu, Kundan Kumar, Inga Berre, Jan Martin Nordbotten, Iuliu Sorin Pop
Place of PublicationCham
PublisherSpringer
Pages1035-1043
Number of pages9
ISBN (Electronic)978-3-319-96415-7
ISBN (Print)978-3-319-96414-0
DOIs
Publication statusPublished - 1 Jan 2019
EventEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 - Voss, Norway
Duration: 25 Sep 201729 Sep 2017

Publication series

NameLecture Notes in Computational Science and Engineering
Volume126
ISSN (Print)1439-7358

Conference

ConferenceEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017
CountryNorway
CityVoss
Period25/09/1729/09/17

Fingerprint

Incompressible Navier-Stokes Equations
Vorticity
Cartesian
Navier Stokes equations
Boundary conditions
Inviscid Limit
Incompressible Viscous Flow
Slip Boundary Condition
Conserve
Cell
Viscous flow
Kinetic energy
Momentum
Mesh
Benchmark
Object

Cite this

Beltman, R., Anthonissen, M., & Koren, B. (2019). Conservative mimetic cut-cell method for incompressible Navier-Stokes equations. In F. A. Radu, K. Kumar, I. Berre, J. M. Nordbotten, & I. S. Pop (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2017 (pp. 1035-1043). (Lecture Notes in Computational Science and Engineering; Vol. 126). Cham: Springer. https://doi.org/10.1007/978-3-319-96415-7_98
Beltman, René ; Anthonissen, Martijn ; Koren, Barry. / Conservative mimetic cut-cell method for incompressible Navier-Stokes equations. Numerical Mathematics and Advanced Applications ENUMATH 2017. editor / Florin Adrian Radu ; Kundan Kumar ; Inga Berre ; Jan Martin Nordbotten ; Iuliu Sorin Pop. Cham : Springer, 2019. pp. 1035-1043 (Lecture Notes in Computational Science and Engineering).
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abstract = "We introduce a mimetic Cartesian cut-cell method for incompressible viscous flow that conserves mass, momentum, and kinetic energy in the inviscid limit, and determines the vorticity such that the global vorticity is consistent with the boundary conditions. In particular we discuss how the no-slip boundary conditions should be applied in a conservative way on objects immersed in the Cartesian mesh. We use the method to compute the flow around a cylinder. We find a good comparison between our results and benchmark results for both a steady and an unsteady test case.",
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Beltman, R, Anthonissen, M & Koren, B 2019, Conservative mimetic cut-cell method for incompressible Navier-Stokes equations. in FA Radu, K Kumar, I Berre, JM Nordbotten & IS Pop (eds), Numerical Mathematics and Advanced Applications ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol. 126, Springer, Cham, pp. 1035-1043, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017, Voss, Norway, 25/09/17. https://doi.org/10.1007/978-3-319-96415-7_98

Conservative mimetic cut-cell method for incompressible Navier-Stokes equations. / Beltman, René; Anthonissen, Martijn; Koren, Barry.

Numerical Mathematics and Advanced Applications ENUMATH 2017. ed. / Florin Adrian Radu; Kundan Kumar; Inga Berre; Jan Martin Nordbotten; Iuliu Sorin Pop. Cham : Springer, 2019. p. 1035-1043 (Lecture Notes in Computational Science and Engineering; Vol. 126).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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N2 - We introduce a mimetic Cartesian cut-cell method for incompressible viscous flow that conserves mass, momentum, and kinetic energy in the inviscid limit, and determines the vorticity such that the global vorticity is consistent with the boundary conditions. In particular we discuss how the no-slip boundary conditions should be applied in a conservative way on objects immersed in the Cartesian mesh. We use the method to compute the flow around a cylinder. We find a good comparison between our results and benchmark results for both a steady and an unsteady test case.

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Beltman R, Anthonissen M, Koren B. Conservative mimetic cut-cell method for incompressible Navier-Stokes equations. In Radu FA, Kumar K, Berre I, Nordbotten JM, Pop IS, editors, Numerical Mathematics and Advanced Applications ENUMATH 2017. Cham: Springer. 2019. p. 1035-1043. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-319-96415-7_98