Fourth-order central compact scheme for the numerical solution of incompressible Navier–Stokes equations

Abdullah Shah*, Hassan Fayyaz, Muhammad Rizwan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

This paper provides an implicit central compact scheme for the numerical solution of incompressible Navier–Stokes equations. The solution procedure is based on the artificial compressibility method that transforms the governing equations into a hyperbolic-parabolic form. A fourth-order central compact scheme with a sixth-order numerical filtering is used for the discretization of convective terms and fourth-order central compact scheme for the viscous terms. Dual-time stepping approach is applied to time discretization with backward Euler difference scheme to the pseudo-time derivative, and three point second-order backward difference scheme to the physical time derivative. An approximate factorization-based alternating direction implicit scheme is used to solve the resulting block tridiagonal system of equations. The accuracy and efficiency of the proposed numerical method is verified by simulating several two-dimensional steady and unsteady benchmark problems.

Original languageEnglish
Pages (from-to)2492-2507
Number of pages16
JournalInternational Journal of Computer Mathematics
Volume94
Issue number12
DOIs
StatePublished - 2 Dec 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • Incompressible Navier–Stokes equations
  • artificial compressibility method
  • central compact scheme
  • dual-time stepping
  • numerical filtering

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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