Afterglows of gamma-ray bursts are observed to produce light curveswith the flux following power law evolution in time. However, recent observations reveal bright flares at times on the order of minutes to days.One proposed explanation for these flares is the interaction of a relativisticblast wave with a circumburst density transition. In this paper, we modelthis type of interaction computationally in one and two dimensions, usinga relativistic hydrodynamics code with adaptive mesh refinement calledram, and analytically in one dimension. We simulate a blast wave travelingin a stellar wind environment that encounters a sudden change indensity, followed by a homogeneous medium, and compute the observedradiation using a synchrotron model. We show that flares are not observablefor an encounter with a sudden density increase, such as a windtermination shock, nor for an encounter with a sudden density decrease.Furthermore, by extending our analysis to two dimensions, we are able toresolve the spreading, collimation, and edge effects of the blast wave as itencounters the change in circumburst medium. In all cases considered inthis paper, we find that a flare will not be observed for any of the densitychanges studied