A new element-by-element method for trajectory calculations with tetrahedral finite element meshes

A new method to track massless particles in a three-dimensional flow field is presented. The method is based on an element-by-element approach coupled with a predictor–corrector shooting scheme and does not use any time step. By analogy with time-dependent schemes, the number of shootings is related to an equivalent number of time steps. The method has been implemented in a finite element framework using unstructured tetrahedral finite element meshes. However, it is general enough so that it can be implemented in finite difference and finite volume frameworks as well. It has been tested on a variety of flow systems namely: the Poiseuille flow in an empty circular pipe, the rotating flow in a stirred tank, the shear flow in a square tank and the flow through a static mixer. Accuracy has been found to depend on the accuracy of the velocity computation, the number of points per element and the level of mesh refinement