A new numerical strategy with space-time adaptivity and error control for multi-scale gas discharge simulations

This paper presents a new resolution strategy for multi-scale gas discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to model plasma discharges, considering drift-diffusion equations and electric field computation. The proposed numerical method provides a time-space accuracy control of the solution, and thus, an effective accurate resolution independent of the fastest physical time scale. Important improvement of computational efficiency is achieved whenever the required time steps go beyond standard stability constraints associated with mesh size or source time scales for the resolution of driftdiffusion equations, whereas stability constraint related to dielectric relaxation time scale is respected but with second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate propagation of highly nonlinear ionizing waves as streamer discharges, as well as highly multi-scale nanosecond repetitively pulsed discharges, describing consistently a broad spectrum of space and time scales as well as different physical scenarios for consecutive discharge/post-discharge phases, out of reach of standard non-adaptive methods.