Minisymposium Presentation

Electrical Treeing is one of the main causes for the degradation of the insulating components of cables: partial discharges occur in a gas-filled defect in the polymer under strong electrical fields.This phenomenon can be modeled by a system of PDEs, describing the movement of charges in the defect and the evolution of the electrical field and potential in both the gas and the solid dielectric material. However, the geometry of the defect makes the problem very challenging: such ramified subdomain with very small diameter can hardly be discretized by a 3D mesh in realistic cases. To overcome this limitation we approximate the treeing as a one-dimensional graph, and derive a mixed-dimensional 3D-1D system of equations, reducing the problem complexity. The numerical solution is based on Mixed FEM for the electrostatic problem and Finite Volumes for the charges movement, and on a splitting to manage the multiphysics coupling with reactive phenomena. The method is implemented in the parallel C++ code Morgana.