A particle localization algorithm on unstructured curvilinear polynomial meshes

Abstract Many particle-based methods require a coupling between particle motion and fluid flows or fields. The particle motion is approximated in phase space, while the fluid flows or fields are calculated on a fixed Eulerian frame of reference. In this work, we present algorithms for locating and tracing particles through curvilinear and unstructured hexahedral meshes. Special attention is given to accurately compute the intersections of particles with polynomial curvilinear faces. We derive two localization algorithms, which locate particles either by tracing in physical space or restricting the tracing step to boundary faces and determining the particles position in reference space. The proposed algorithms are validated by three-dimensional charged particle simulations in electromagnetic fields.