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This paper presents a new resolution strategy for multi-scale streamerdischarge simulations based on a second order time adaptive integration andspace adaptive multiresolution. A classical fluid model is used to describeplasma discharges, considering drift-diffusion equations and the computation ofelectric field. The proposed numerical method provides a time-space accuracycontrol of the solution, and thus, an effective accurate resolution independentof the fastest physical time scale. An important improvement of thecomputational efficiency is achieved whenever the required time steps go beyondstandard stability constraints associated with mesh size or source time scalesfor the resolution of the drift-diffusion equations, whereas the stabilityconstraint related to the dielectric relaxation time scale is respected butwith a second order precision. Numerical illustrations show that the strategycan be efficiently applied to simulate the propagation of highly nonlinearionizing waves as streamer discharges, as well as highly multi-scale nanosecondrepetitively pulsed discharges, describing consistently a broad spectrum ofspace and time scales as well as different physical scenarios for consecutivedischarge/post-discharge phases, out of reach of standard non-adaptive methods.

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