A comparison of methods for interpolating chaotic flows from discrete velocity data

In this paper we consider a variety of schemes for performing interpolation in space and time to allow particle trajectories to be integrated from a velocity field given only on a discrete collection of data points in space and time. Using a widely-studied model of chaotic advection as a test case we give a method for quantifying the quality of interpolation methods and apply this to a variety of interpolation schemes in space only and in both space and time. It is shown that the performance of a method when interpolating in space is not a reliable predictor of its performance when interpolation in time is added. It is demonstrated that a method using bicubic spatial interpolation together with third-order Lagrange polynomials in time gives excellent accuracy at very modest computational expense compared to other methods.