We present and compare six simulation codes for positive streamer discharges from six different research groups. Four groups use a fully self-implemented code and two make use of COMSOL Multiphysics ®. Three test cases are considered, in which axisymmetric positive streamers are simulated in dry air at 1 bar and 300 K in an undervolted gap. All groups use the same fluid model with the same transport coefficients. The first test case includes a relatively high background density of electrons and ions without photoionization. When each group uses their standard grid resolution, results show considerable variation, particularly in the prediction of streamer velocities and maximal electric fields. However, for sufficiently fine grids good agreement is reached between several codes. The second test includes a lower background ionization density, and oscillations in the streamer properties, branching and numerical instabilities are observed. By using a finer grid spacing some groups were able to reach reasonable agreement in their results, without oscillations. The third test case includes photoionization, using both Luque's and Bourdon's Helmholtz approximation. The results agree reasonably well, and the numerical differences appear to be more significant than the type of Helmholtz approximation. Computing times, used hardware and numerical parameters are described for each code and test case. We provide detailed output in the supplementary data, so that other streamer codes can be compared to the results presented here.

This paper is mainly devoted to the comparison between the calculation and experimental results of primary and secondary streamer development in a point-to-plane positive corona discharge in dry air at atmospheric pressure. The qualitative agreement between experimental and calculation results based on the hydrodynamics approximation shows that the O radical is mainly produced in the secondary streamer which is in good agreement with the recent literature measurements using TALIF diagnostics. However, the O radical production yield (in terms of radicals produced per energy injected) is more efficient in the primary streamer than in the secondary one. The main positive corona discharge characteristics are revisited using fast electrical and optical ICCD and streak camera measurements. The calculation shows two streamer radii of, respectively, 10 µm (associated with the radial extension of a high electron density region) and 200 µm (corresponding to the extension of the radial space charge electric field).

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The present paper shows that in the case of a micro-discharge modelling using the hydrodynamics assumption, the second order fluid model involving the complete electron momentum conservation equation must be used in order to better quantify the radical formation in a micro-discharge applied to air pollution control. The present results show large differences in the micro-discharge parameters (such as velocity and electron density) between the three tested hydrodynamics models: the classical first order model using the local electric field approximation and two second order models using the local energy approximation with or without the drift–diffusion approximation. The tests have been carried out in the case of a wire-to-plane corona reactor filled with a typical flue gas (76% N2, 12% CO2, 6% O2, 6% H2O) at atmospheric pressure and ambient temperature. The simulation of the micro-discharge dynamics is performed using a 1.5D numerical streamer model coupled with a simple chemical kinetics model involving 31 species (charged and neutral particles in their fundamental or metastable state) reacting following 29 selected chemical reactions.

This paper concerns the 3D simulation of corona discharge using high performance computing (HPC) managed with the message passing interface (MPI) library. In the field of finite volume methods applied on non-adaptive mesh grids and in the case of a specific 3D dynamic benchmark test devoted to streamer studies, the great efficiency of the iterative R&B SOR and BiCGSTAB methods versus the direct MUMPS method was clearly demonstrated in solving the Poisson equation using HPC resources. The optimization of the parallelization and the resulting scalability was undertaken as a function of the HPC architecture for a number of mesh cells ranging from 8 to 512 million and a number of cores ranging from 20 to 1600. The R&B SOR method remains at least about four times faster than the BiCGSTAB method and requires significantly less memory for all tested situations. The R&B SOR method was then implemented in a 3D MPI parallelized code that solves the classical first order model of an atmospheric pressure corona discharge in air. The 3D code capabilities were tested by following the development of one, two and four coplanar streamers generated by initial plasma spots for 6 ns. The preliminary results obtained allowed us to follow in detail the formation of the tree structure of a corona discharge and the effects of the mutual interactions between the streamers in terms of streamer velocity, trajectory and diameter. The computing time for 64 million of mesh cells distributed over 1000 cores using the MPI procedures is about 30 min ns −1 , regardless of the number of streamers.

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This paper is a contribution to the fluid modelling and simulation of the spontaneous branching of an initial mono-filamentary negative streamer propagating in molecular nitrogen at atmospheric pressure. The effects of both numerical diffusion and physical anisotropic diffusion on the branching structure are studied. We used MUSCL-type flux limiters where an artificial amount of numerical diffusion can be introduced through the choice of the value of a characteristic slope parameter. It was shown that a small amount of numerical diffusion can inhibit the spontaneous streamer branching. This means that the use of a high-order numerical scheme preventing the numerical diffusion and dispersion is a major parameter that must be taken into account in the interpretation of the simulated streamer development and splitting. This paper also clearly shows that the consideration of the anisotropy of electron diffusion affects the streamer head structure in comparison with the isotropic diffusion case. This especially occurs for electrons in gases presenting a large difference between the longitudinal and transversal diffusion coefficients as in N2 or in air.