Math @ Duke

Publications [#246918] of JianGuo Liu
Papers Published
 Weinan, E; Liu, JG, Projection method II: GodunovRyabenki analysis,
Siam Journal on Numerical Analysis, vol. 33 no. 4
(1996),
pp. 15971621, Society for Industrial & Applied Mathematics (SIAM) [doi]
(last updated on 2019/02/17)
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 GodunovRyabenki 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 finitedifference method for the NavierStokes equation even in the presence of boundaries. As an example, we analyze the secondorder 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 secondorder KimMoin method.


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