The Accuracy and Performance of Parallel In-Element Particle Tracking Methods

This paper presents a study of the accuracy and performance issues involved in parallel, in-element particle tracking methods. Eulerian-Lagrangian methods (ELM) are employed to solve a variety of partial differential equations (PDEs), and is well suited to solution of advection/convection-dominated PDEs. The Lagrangian step employed by these methods is used to more accurately handle the advection/convection term. A necessary feature of these methods is the use of particle tracking techniques for computing advection accurately in the Lagrangian step. The technique, “in-element” particle tracking, traces fictitious particles on an element-by-element basis. Building on the serial version of this method, in this paper we a parallel in-element particle tracking algorithm. The approach used can be generalized to other methods based on particle tracking—including applications from visualization, N-body problems, and reacting and multi-phase flows.