American Institute of Mathematical Sciences

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August  2005, 5(3): 817-840. doi: 10.3934/dcdsb.2005.5.817

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, United States, United States

Received  September 2004 Revised  January 2005 Published  May 2005

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.
Keywords: Naiver-Stoke equations, Normal Mode Analysis, Spectral approximations., Incompressibility, Fractional step methods, projection methods.
Mathematics Subject Classification: 65N35, 76D0.
Citation: Jae-Hong Pyo, Jie Shen. Normal mode analysis of second-order projection methods for incompressible flows. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 817-840. doi: 10.3934/dcdsb.2005.5.817
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