Particle-In-Cell Algorithm on Unstructured Tetrahedral Meshes

New unstructured Particle-In-Cell method on tetrahedral grids is presented. In this method the electric potential on cell vertices is evaluated using Gauss’ law applied to the indirect dual cell formed by connecting centroids of tetrahedra with corresponding face centroids and edge centers. The control-volume discretization follows a finite volume Multi Point Flux Approximation method. The implementation of boundary conditions such as Dirichlet, Neumann and external circuit boundary conditions is presented. The resulting matrix equation for the nodal potential is solved with a restarted GMRES algorithm with ILU(0) preconditioner. The GMRES algorithm is OpenMP parallelized using a combination of node coloring and level scheduling approaches for better computational efficiency. The electric field on vertices is evaluated using the gradient theorem applied to the indirect dual cell. The resulting expression for electric field is consistent with the earlier algorithm that was derived using Delaunay-Voronoi grids ¹. Boundary conditions and the algorithms for injection, particle loading, particle motion, and particle tracking are implemented for unstructured tetrahedral grids in the code developed at WPI.