Projection method II: Godunov-Ryabenki analysis

E. Weinan, Jian Guo Liu

Research output: Contribution to journalArticle

35 Scopus citations

Abstract

This is the second of a series of papers on the subject of projection methods for viscous incompressible flow calculations. The purpose of the present paper is to explain why the accuracy of the velocity approximation is not affected by (1) the numerical boundary layers in the approximation of pressure and the intermediate velocity field and (2) the noncommutativity of the projection operator and the laplacian. This is done by using a Godunov-Ryabenki type of analysis in a rigorous fashion. By doing so, we hope to be able to convey the message that normal mode analysis is basically sufficient for understanding the stability and accuracy of a finite-difference method for the Navier-Stokes equation even in the presence of boundaries. As an example, we analyze the second-order projection method based on pressure increment formulations used by van Kan and Bell, Colella, and Glaz. The leading order error term in this case is of O(Δt) and behaves as high frequency oscillations over the whole domain, compared with the O(Δt1/2) numerical boundary layers found in the second-order Kim-Moin method.

Original languageEnglish (US)
Pages (from-to)1597-1621
Number of pages25
JournalSIAM Journal on Numerical Analysis
Volume33
Issue number4
DOIs
StatePublished - Aug 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Convergence
  • Godunov-Ryabenki analysis
  • Numerical boundary layers
  • Projection method
  • Viscous incompressible flows

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