Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids

Handle URI:
http://hdl.handle.net/10754/625751
Title:
Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids
Authors:
Chen, Huangxin; Sun, Shuyu ( 0000-0002-3078-864X ) ; Zhang, Tao
Abstract:
In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.
KAUST Department:
Computational Transport Phenomena Lab; Physical Sciences and Engineering (PSE) Division
Citation:
Chen H, Sun S, Zhang T (2017) Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids. Journal of Scientific Computing. Available: http://dx.doi.org/10.1007/s10915-017-0543-3.
Publisher:
Springer Nature
Journal:
Journal of Scientific Computing
Issue Date:
1-Sep-2017
DOI:
10.1007/s10915-017-0543-3
Type:
Article
ISSN:
0885-7474; 1573-7691
Sponsors:
The work of Huangxin Chen was supported by the NSF of China (Grant Nos. 11771363, 91630204, 51661135011) and Program for Prominent Young Talents in Fujian Province University. Shuyu Sun acknowledges that this work is supported by the KAUST research fund awarded to the Computational Transport Phenomena Laboratory at KAUST through the Grant BAS/1/1351-01-01.
Additional Links:
https://link.springer.com/article/10.1007%2Fs10915-017-0543-3
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab

Full metadata record

DC FieldValue Language
dc.contributor.authorChen, Huangxinen
dc.contributor.authorSun, Shuyuen
dc.contributor.authorZhang, Taoen
dc.date.accessioned2017-10-03T12:49:37Z-
dc.date.available2017-10-03T12:49:37Z-
dc.date.issued2017-09-01en
dc.identifier.citationChen H, Sun S, Zhang T (2017) Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids. Journal of Scientific Computing. Available: http://dx.doi.org/10.1007/s10915-017-0543-3.en
dc.identifier.issn0885-7474en
dc.identifier.issn1573-7691en
dc.identifier.doi10.1007/s10915-017-0543-3en
dc.identifier.urihttp://hdl.handle.net/10754/625751-
dc.description.abstractIn this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.en
dc.description.sponsorshipThe work of Huangxin Chen was supported by the NSF of China (Grant Nos. 11771363, 91630204, 51661135011) and Program for Prominent Young Talents in Fujian Province University. Shuyu Sun acknowledges that this work is supported by the KAUST research fund awarded to the Computational Transport Phenomena Laboratory at KAUST through the Grant BAS/1/1351-01-01.en
dc.publisherSpringer Natureen
dc.relation.urlhttps://link.springer.com/article/10.1007%2Fs10915-017-0543-3en
dc.subjectNavier–Stokes equationen
dc.subjectFinite difference methodsen
dc.subjectStaggered gridsen
dc.subjectLinear implicit schemeen
dc.subjectProjection methoden
dc.subjectUpwind schemeen
dc.subjectEnergy stabilityen
dc.titleEnergy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Gridsen
dc.typeArticleen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalJournal of Scientific Computingen
dc.contributor.institutionSchool of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, Chinaen
kaust.authorSun, Shuyuen
kaust.authorZhang, Taoen
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