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

TL;DR

This paper introduces a novel adaptive numerical strategy combining space-time adaptivity and error control for efficient multi-scale streamer discharge simulations, improving accuracy and computational efficiency over traditional methods.

Contribution

The paper develops a second order adaptive integration and multiresolution approach that effectively handles multiple scales in plasma discharge simulations with improved accuracy and efficiency.

Findings

Efficiently simulates nonlinear ionizing wave propagation.

Handles broad spectrum of space and time scales.

Outperforms standard non-adaptive methods in complex scenarios.

Abstract

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift-diffusion equations and the computation of electric field. 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. An important improvement of the 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 the drift-diffusion equations, whereas the stability constraint related to the dielectric relaxation time scale is respected but with a second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate the 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.