Efficient preconditioning for the simulation of nanosecond discharge using Jacobian-Free Newton Krylov Methods

A novel methodology is presented for the simulation of streamer discharges. The governing equations consist of the drift-diffusion model with local-field approximation, which is applied for the transport of all charged species. Electrons, one positive ion, and one negative ion are considered along with a simplified air-plasma chemistry that includes ionization, recombination, attachment, and detachment processes. Nonlinear boundary conditions with secondary emissions are also included. The governing equations are integrated in time in a fully coupled manner with the use of a Jacobian Free Newton Krylov (JFNK) method and a third-order implicit formulation. A suitable preconditioning framework based on operator splitting is developed and applied towards axisymmetric pin-to-pin discharge simulations in atmospheric air. The solver is implemented in parallel with the Portable Extensible Toolkit for Scientific Computation (PETSc). The governing equations are integrated successfully using time steps of up to 20 picoseconds and mesh resolutions of up to 0.6 micron, exceeding drift and dielectric time scales. The preconditioner was found to be very effective as shown by metrics, which include Newton iterations, Krylov iterations and wallclock times.