An Error Analysis of Streaklines as Curves

A streakline is a visible curve consisting of fluid particles which emerged continuously from a fixed point in a given flow field. In many cases we do not know the exact velocity field but can get an approximate velocity field. The computation of streaklines includes the discretization error as well as the error caused by the approximate velocity field. We give an error analysis of streaklines as curves in terms of τ and h, discretization parameters of the streakline and of the velocity field. We show that, when the velocity field is approximated piecewise linearly, a computation scheme based on the Heun method is the best choice to approximate streaklines from the viewpoint of accuracy and efficiency. We present simulation results of streaklines emerging from the surface of a circular cylinder at Reynolds numbers 100 and 10000.