An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries

We review a scalable two- and three-dimensional computer code for low-temperature plasma simulations in multi-material complex geometries. Our approach is based on embedded boundary (EB) finite volume discretizations of the minimal fluid-plasma model on adaptive Cartesian grids, extended to also account for charging of insulating surfaces. We discuss the spatial and temporal discretization methods, and show that the resulting overall method is second order convergent, monotone, and conservative (for smooth solutions). Weak scalability with parallel efficiencies over 70\% are demonstrated up to 8192 cores and more than one billion cells. We then demonstrate the use of adaptive mesh refinement in multiple two- and three-dimensional simulation examples at modest cores counts. The examples include two-dimensional simulations of surface streamers along insulators with surface roughness; fully three-dimensional simulations of filaments in experimentally realizable pin-plane geometries, and three-dimensional simulations of positive plasma discharges in multi-material complex geometries. The largest computational example uses up to $800$ million mesh cells with billions of unknowns on $4096$ computing cores. Our use of computer-aided design (CAD) and constructive solid geometry (CSG) combined with capabilities for parallel computing offers possibilities for performing three-dimensional transient plasma-fluid simulations, also in multi-material complex geometries at moderate pressures and comparatively large scale.Comment: 40 pages, 21 figure

Adaptive multiscale methods for 3D streamer discharges in air

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.Comment: 17 pages, 5 figure

3D fluid modeling of positive streamer discharges in air with stochastic photoionization

Streamer discharges are thin plasma channels that precede lightning and sparks. They usually evolve in bundles as stochastic tree-like structures and are inherently difficult to model due to their multiscale nature. In this paper, we perform a computer investigation of positive streamer discharges in air using contemporary photoionization models. We report on three-dimensional computer simulations under conditions that are available in laboratory spark-gap experiments. The solutions demonstrate a multiscale morphology consisting of streamer fluctuations, branching, and the formation of a discharge tree. Some branches are comparatively thick and noisy, while others are thin, smooth, and carry electric fields exceeding $250\,\textrm{kV/cm}$ at their tips. Our results are consistent with past experiments and clarify the puzzling branching dynamics and stochastic morphology of positive streamer discharges.Comment: 14 pages, 3 figures, 2 movie

Stochastic and self-consistent 3D modeling of streamer discharge trees with Kinetic Monte Carlo

This paper contains the foundation for a new Particle-In-Cell model for gas discharges, based on Ito diffusion and Kinetic Monte Carlo (KMC). In the new model the electrons are described with a microscopic drift-diffusion model rather than a macroscopic one. We discuss the connection of the Ito-KMC model to the equations of fluctuating hydrodynamics and the advection-diffusion-reaction equation which is conventionally used for simulating streamer discharges. The new model is coupled to a particle description of photoionization, providing a non-kinetic all-particle method with several attractive properties, such as: 1) Taking the same input as a fluid model, e.g. mobility coefficients, diffusion coefficients, and reaction rates. 2) Guaranteed non-negative densities. 3) Intrinsic support for reactive and diffusive fluctuations. 4) Exceptional stability properties. The model is implemented as a particle-mesh model on cut-cell grids with Cartesian adaptive mesh refinement. Positive streamer discharges in atmospheric air are considered as the primary application example, and we demonstrate that we can self-consistently simulate large discharge trees.Comment: 29 pages, 16 figure

What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations

Electric streamer discharges (streamers) in the air are a very important stage of lightning, taking place before formation of the leader discharge, and with which an electric discharge starts from conducting objects which enhance the background electric field, such as airplanes. Despite years of research, it is still not well understood what mechanism determines the values of a streamer’s parameters, such as its radius and propagation velocity. The novel Streamer Parameter Model (SPM) was made to explain this mechanism, and to provide a way to efficiently calculate streamer parameters. Previously, we demonstrated that SPM results compared well with a limited set of experimental data. In this article, we compare SPM predictions to the published hydrodynamic simulation (HDS) results. Keywords: atmospheric electricity; electric streamer discharges; streamer theory; streamer parameters; plasma instabilities; partially-ionized plasmaspublishedVersio

Evolution of positive streamers in air over non-planar dielectrics: Experiments and simulations

We study positive streamers in air propagating along polycarbonate dielectric plates with and without small-scale surface profiles. The streamer development was documented using light-sensitive high-speed cameras and a photo-multiplier tube, and the experimental results were compared with 2D fluid streamer simulations. Two profiles were tested, one with 0.5 mm deep semi-circular corrugations and one with 0.5 mm deep rectangular corrugations. A non-profiled surface was used as a reference. Both experiments and simulations show that the surface profiles lead to significantly slower surface streamers, and also reduce their length. The rectangular-cut profile obstructs the surface streamer more than the semi-circular profile. We find quantitative agreement between simulations and experiments. For the surface with rectangular grooves, the simulations also reveal a complex propagation mechanism where new positive streamers re-ignite inside the surface profile corrugations. The results are of importance for technological applications involving streamers and solid dielectrics.Comment: 15 pages, 12 figure

A kinetic Monte Carlo study of positive streamer interaction with complex dielectric surfaces

We present a computational study of positive streamers in air propagating over dielectric plates with square channels running orthogonal to the propagation direction. The study uses a newly developed non-kinetic Particle-In-Cell model based on Îto diffusion and kinetic Monte Carlo, which does not introduce artificial smoothing of the plasma density or photo-electron distributions. These capabilities permit the computational study to use high-resolution grids with large time steps, and also incorporates geometric shielding for particle and photon transport processes. We perform Cartesian 2D simulations for channel dimensions ranging from 250 µm to 2 mm, and track streamers over a distance of 4 cm and times ranging up to 300 ns, for various voltages ranging from 15 kV to 30 kV. These baseline simulations are supplemented by additional studies on the effects of transparency to ionizing radiation, streamer reignition, dielectric permittivity, and 3D effects. The computer simulations show: 1) Larger channels restrict streamer propagation more efficiently than narrow channels, and can lead to arrested surface streamers. 2) Geometric shielding of ionizing radiation substantially reduces the number of starting electrons in neighboring channels, and thus also reduces the onset point of streamer reignition. 3) Decreasing the streamer channel separation leads to slower streamers. 4) Increasing the dielectric permittivity increases the discharge velocity. The results are of generic value to fields of research involving streamer-dielectric interactions, and in particular for high-voltage technology where streamer termination is desirable. © 2023 The Author(s). Published by IOP Publishing Ltd. Author keywords dielectric; kinetic Monte Carlo; Particle-In-Cell; streamer; surface profileA kinetic Monte Carlo study of positive streamer interaction with complex dielectric surfacespublishedVersio

Streamer Propagation along Profiled Insulator Surfaces under Positive Impulse Voltages

Controlling discharge growth on insulator surfaces is important in high voltage gaseous insulation systems. In this study, the effect of small-scale surface profiles on streamer discharge propagation is examined experimentally. The experimental test objects were 5x72x150 mm polycarbonate plates with and without machined surface profiles. One test object had a surface with 0.5 mm deep semi-circular corrugations, while the other profile had 0.5 mm deep rectangular corrugations. The semi-circular profile increased the surface area with 20 %, while the rectangular profile increased the area with 110 %. A plain surface was also examined as a reference. Positive impulse voltages were applied to a 1 mm thick disk electrode placed 2 mm above the insulator. The insulator was placed in a grounded aluminium casing. The streamer development was imaged with a light-sensitive high-speed camera. Surface charges left on the surface after the impulse were examined using an electrostatic probe and simulations of saturation charge. The rectangular surface profile reduced the streamer range significantly, which suggests an effect of added surface area. Imaging indicated that the wavelike surface streamers follow the profiles closely. Surface potential measurements showed a saddle-shaped distributions, with values in line with saturation charge computations.Streamer Propagation along Profiled Insulator Surfaces under Positive Impulse VoltagespublishedVersio

chombo-discharge: An AMR code for gas discharge simulations in complex geometries

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