Projection method II: Godunov-Ryabenki analysis
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.
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Related Subject Headings
- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics