A 15-point high-order compact scheme with multigrid computation for solving 3D convection diffusion equations

Yin Wang, Su Yu, Ruxin Dai, Jun Zhang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We propose a method with sixth-order accuracy to solve the three-dimensional (3D) convection diffusion equation. We first use a 15-point fourth-order compact discretization scheme to obtain fourth-order solutions on both fine and coarse grids using the multigrid method. Then an iterative mesh refinement technique combined with Richardson extrapolation is used to approximate the sixth-order accurate solution on the fine grid. Numerical results are presented for a variety of test cases to demonstrate the efficiency and accuracy of the proposed method, compared with the standard fourth-order compact scheme.

Original languageEnglish
Pages (from-to)411-423
Number of pages13
JournalInternational Journal of Computer Mathematics
Volume92
Issue number2
DOIs
StatePublished - Feb 1 2015

Bibliographical note

Funding Information:
This author’s research work was supported in part by NSF under grant CNS-1157162, and in part by NVIDIA research CUDA Teaching Center.

Publisher Copyright:
© 2014, © 2014 Taylor & Francis.

Keywords

  • 15-point stencil
  • Reynolds number
  • convection diffusion equation
  • multigrid method
  • sixth-order compact scheme

ASJC Scopus subject areas

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

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