Normal mode analysis of second-order projection methods forincompressible flows

Jae-Hong Pyo; Jie Shen

doi:10.3934/dcdsb.2005.5.817

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2005, Volume 5, Issue 3: 817-840. Doi: 10.3934/dcdsb.2005.5.817

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Normal mode analysis of second-order projection methods for incompressible flows

Jae-Hong Pyo^1, and
Jie Shen^1,

1.
Department of Mathematics, Purdue University, West Lafayette , IN 47907

Received: August 31, 2004

Revised: December 31, 2004

Published: July 2005

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Abstract

A rigorous normal mode error analysis is carried out for two second-order projection type methods. It is shown that although the two schemes provide second-order accuracy for the velocity in $\L^2$-norm, their accuracies for the velocity in $\H^1$-norm and for the pressure in $L^2$-norm are different, and only the consistent splitting scheme introduced in [6] provides full second-order accuracy for all variable in their natural norms. The advantages and disadvantages of the normal mode analysis vs. the energy method are also elaborated.

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Mathematics Subject Classification: 65N35, 76D05.

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