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The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number

Published online by Cambridge University Press:  03 June 2015

Kazufumi Ito ,
Zhilin Li  and
Zhonghua Qiao
Kazufumi Ito*
Affiliation:
Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA
Zhilin Li*
Affiliation:
Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA School of Mathematical Sciences, Nanjing Normal University, No. 1 Wenyuan Road, Yadong New District, Nanjing 210046, China
Zhonghua Qiao*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
*
URL: http://www4.ncsu.edu/∼zhilin/, Email: kito@math.ncsu.edu
Corresponding author. Email: zhilin@math.ncsu.edu
Email: zqiao@hkbu.edu.hk
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Abstract

In this paper, numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented. To carry out such analysis, at each time step, we need to solve the incompressible Navier-Stokes equations on irregular domains twice, one for the primary variables; the other is for the sensitivity variables with homogeneous boundary conditions. The Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular domains. One of the most important contribution of this paper is that our analysis can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the obstacle. Some interesting experiments are shown to illustrate how the critical Reynolds number varies with different geometric settings.

Keywords

65M0665M1276T05Navier-Stokes equationssensitivity analysisflow past cylinderembedding techniqueimmersed interface methodirregular domainaugmented systemprojection methodfluid-solid interaction
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 1 , February 2012 , pp. 21 - 35
Copyright
Copyright © Global-Science Press 2012

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