A continuous sensitivity equation method for time-dependent incompressible laminar flows

Abstract

This paper presents a general sensitivity equation method (SEM) for time dependent incompressible laminar flows. The formulation accounts for complex parameter dependence and is suitable for a wide range of problems. The SEM formulation is verified on a problem with a closed form solution. Systematic grid convergence studies confirm the theoretical rates of convergence in both space and time. The methodology is then applied to pulsed flow around a square cylinder. The flow starts with symmetrical vortex shedding then transitions to the traditional Von Karman street (alternate vortex shedding). Simulations indicate that the transition phase manifests itself earlier in the sensitivity fields than in the flow field itself. Sensitivities are then demonstrated for fast evaluation of nearby flows and uncertainty analysis. Copyright © 2005 John Wiley & Sons, Ltd.