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

In this paper, numerical sensitivity analysis with respect to theReynolds number for the flow past obstacle problem is presented.To carry out such analysis, at each time step, we need to solve theincompressible Navier-Stokes equations on irregular domains twice, one for theprimary variables; the other is for the sensitivity variables withhomogeneous boundary conditions.The Navier-Stokes solver is the augmented immersedinterface method for Navier-Stokes equations on irregular domains.One of the most important contributions of this paper is that our analysiscan predict the critical Reynolds number at which the vortex shadingbegins to develop in the wake of the obstacle. Some interesting experiments are shownto illustrate how the critical Reynolds number varies with differentgeometric settings.