A particle tracking algorithm for parallel finite element applications

Numerical simulations of a particle tracking algorithm on parallel unstructured finite element grids are presented. The algorithm is designed to work for both 2D and 3D applications. To determine the position of the particle relative to the mesh, a new point-locating algorithm is proposed. The advection of the particle is performed on the physical domain in order to treat completely unstructured grids. As a consequence, the inversion of the isoparametric finite element mapping is requested. We comply with this demand implicitly using Newton-Raphson's iteration for linear, quadratic, bi-quadratic and tri-quadratic finite elements, and several element geometries, including quadrilaterals, triangles, tetrahedra, wedges and hexahedra. To investigate the performances of the proposed algorithm, results of standard numerical tests are shown, together with a fluid flow application that exemplifies an instance of a particle tracking problem.