  We present an novel algorithm for tracking massless solid particles in a
divergence-free velocity field that is only available at discrete points in
space and time such as those arising from a direct numerical simulation of
Navier-Stokes. The algorithm creates a divergence-free approximation to the
numerical field using matrix valued radial basis functions, which is integrated
in time using a volume-preserving map. The resulting method is able to
calculate accurate trajectories in a helical vortex using much larger
step-sizes and a far lower number of interpolation points which results in a
more efficient algorithm compared to a conventional scheme.
