Nonlinear particle tracking for high-order elements

The problem of calculating particle trajectories on unstructured meshes usi ng a high-order polynomial approximation of the velocity field is addressed . The calculation of the particle trajectory is based on a Runge-Kutta inte gration in time. A convenient way of implementing high-order approximations is to employ an auxiliary mapping that transforms a finite element into a topologically equivalent parent element within a normalized parametric spac e. This presents two possible choices of space in which to perform the time integration of the particle position: the physical space or the parametric space. We present algorithms for implementing both particle tracking strat egies using high-order elements and discuss their merits. The main drawback of both methods is their reliance on nonlinear procedures to calculate the particle trajectory. A novel alternative hybrid approach that advances a p article in both the physical and the parametric space without requiring non linear iterations is proposed. The error introduced by the alternative line arized procedures and their effect in the rate of convergence of the time i ntegration is discussed. Finally, the performance of the different algorith ms is compared using a set of analytical and computational, linear and high -order, velocity fields. (C) 2001 Academic Press.