A practical finite difference scheme for the Navier–Stokes equation on curved surfaces in R3

Junxiang Yang, Yibao Li, Junseok Kim

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We present a practical finite difference scheme for the incompressible Navier–Stokes equation on curved surfaces in three-dimensional space. In the proposed method, the curved surface is embedded in a narrow band domain and the governing equation is extended to the narrow band domain. We use the standard seven-point stencil for the Laplace operator instead of a discrete Laplacian–Beltrami operator by using the closet point method and pseudo-Neumann boundary condition. The well-known projection method is used to solve the incompressible Navier–Stokes equation in the narrow band domain. To make the velocity field be parallel to the surface, a velocity correction step is used. Various numerical experiments, such as the divergence-free test, the convergence rate, and the energy dissipation, are performed on curved surfaces, which demonstrated that our proposed method is robust and practical.

Original languageEnglish
Article number109403
JournalJournal of Computational Physics
Volume411
DOIs
Publication statusPublished - 2020 Jun 15

Keywords

  • Closest-point method
  • Curved surfaces
  • Incompressible Navier–Stokes equation
  • Narrow band domain
  • Projection method

ASJC Scopus subject areas

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

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