Existence and stability in the virtual interpolation point method for the Stokes equations

Seong Kwan Park, Gahyung Jo, Hi Jun Choe

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, we propose a novel virtual interpolation point (VIP) method formulating discrete Stokes equations. We have formed virtual staggered structure for velocity and pressure from the actual computation node set. The VIP method by a point collocation scheme is well suited for meshfree scheme because the approximation comes from smooth kernels and kernels can be differentiated directly. This paper highlights our contribution to a stable flow computation without explicit structure of staggered grid. Our method eliminates the need to construct explicit staggered grid. Instead, virtual interpolation nodes play key roles in discretizing the conservative quantities of the Stokes equations. We have proved the inf-sup condition for VIP method with virtual structure of staggered grid and thus the existence and stability of discrete solutions follow.

Original languageEnglish
Pages (from-to)535-549
Number of pages15
JournalJournal of Computational Physics
Volume307
DOIs
Publication statusPublished - 2016 Feb 15

Fingerprint

Convergence of numerical methods
interpolation
Interpolation
grids
collocation
approximation

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Existence and stability in the virtual interpolation point method for the Stokes equations. / Park, Seong Kwan; Jo, Gahyung; Choe, Hi Jun.

In: Journal of Computational Physics, Vol. 307, 15.02.2016, p. 535-549.

Research output: Contribution to journalArticle

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AB - In this paper, we propose a novel virtual interpolation point (VIP) method formulating discrete Stokes equations. We have formed virtual staggered structure for velocity and pressure from the actual computation node set. The VIP method by a point collocation scheme is well suited for meshfree scheme because the approximation comes from smooth kernels and kernels can be differentiated directly. This paper highlights our contribution to a stable flow computation without explicit structure of staggered grid. Our method eliminates the need to construct explicit staggered grid. Instead, virtual interpolation nodes play key roles in discretizing the conservative quantities of the Stokes equations. We have proved the inf-sup condition for VIP method with virtual structure of staggered grid and thus the existence and stability of discrete solutions follow.

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