Volume 4, Issue 1
The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number

Kazufumi Ito, Zhilin Li & Zhonghua Qiao

Adv. Appl. Math. Mech., 4 (2012), pp. 21-35.

Published online: 2012-04

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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 contributions 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

Navier-Stokes equations, sensitivity analysis, flow past cylinder, embedding technique, immersed interface method, irregular domain, augmented system, projection method, fluid-solid interaction.

  • AMS Subject Headings

65M06, 65M12, 76T05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-21, author = {Kazufumi Ito , and Zhilin Li , and Qiao , Zhonghua}, title = {The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {1}, pages = {21--35}, 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 contributions 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.11-m1110}, url = {http://global-sci.org/intro/article_detail/aamm/104.html} }
TY - JOUR T1 - The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number AU - Kazufumi Ito , AU - Zhilin Li , AU - Qiao , Zhonghua JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 21 EP - 35 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.11-m1110 UR - https://global-sci.org/intro/article_detail/aamm/104.html KW - Navier-Stokes equations, sensitivity analysis, flow past cylinder, embedding technique, immersed interface method, irregular domain, augmented system, projection method, fluid-solid interaction. AB -

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 contributions 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.

Kazufumi Ito, Zhilin Li & Zhonghua Qiao. (1970). The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number. Advances in Applied Mathematics and Mechanics. 4 (1). 21-35. doi:10.4208/aamm.11-m1110
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