Adaptive multiscale methods for 3D streamer discharges in air

TL;DR

This paper introduces adaptive implicit-explicit methods for efficient 3D streamer discharge simulations in air, enabling larger time steps for electric and radiative transport equations without significant accuracy loss, thus reducing computational costs.

Contribution

It develops strategies for synchronizing different time step advances in 3D streamer simulations, including error diagnostics for electric and radiative transport equations, improving computational efficiency.

Findings

Longer time steps for electric fields are valid under certain conditions.

Radiative transport equations do not require fine time resolution.

Simulation of 3D branching streamers with 700 million grid cells demonstrated.

Abstract

We discuss spatially and temporally adaptive implicit-explicit (IMEX) methods for parallel simulations of three-dimensional fluid streamer discharges in atmospheric air. We examine strategies for advancing the fluid equations and elliptic transport equations (e.g. Poisson) with different time steps, synchronizing them on a global physical time scale which is taken to be proportional to the dielectric relaxation time. The use of a longer time step for the electric field leads to numerical errors that can be diagnosed, and we quantify the conditions where this simplification is valid. Likewise, using a three-term Helmholtz model for radiative transport, the same error diagnostics show that the radiative transport equations do not need to be resolved on time scales finer than the dielectric relaxation time. Elliptic equations are bottlenecks for most streamer simulation codes, and the results presented here potentially provide computational savings. Finally, a computational example of 3D branching streamers in a needle-plane geometry that uses up to 700 million grid cells is presented.