title: The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number.
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.
authors.affiliation: Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA.
authors.forename: Kazufumi
authors.initials: K
authors.lastname: Ito
authors.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.
authors.forename: Zhilin
authors.initials: Z
authors.lastname: Li
authors.affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
authors.forename: Zhonghua
authors.initials: Z
authors.lastname: Qiao
keywords: Navier-Stokes equations; augmented system; embedding technique; flow past cylinder; fluid-solid interaction; immersed interface method; irregular domain; projection method; sensitivity analysis