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 presents a parallel framework for simulating fluids with the Smoothed Particle Hydrodynamics (SPH) method. For low computational costs per simulation step, efficient parallel neighbourhood queries are proposed and compared. To further minimize the computing time for entire simulation sequences, strategies for maximizing the time step and the respective consequences for parallel implementations are investigated. The presented experiments illustrate that the parallel framework can efficiently compute large numbers of time steps for large scenarios. In the context of neighbourhood queries, the paper presents optimizations for two efficient instances of uniform grids, that is, spatial hashing and index sort. For implementations on parallel architectures with shared memory, the paper discusses techniques with improved cache-hit rate and reduced memory transfer. The performance of the parallel implementations of both optimized data structures is compared. The proposed solutions focus on systems with multiple CPUs. Benefits and challenges of potential GPU implementations are only briefly discussed.

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Using theoretical and experimental methods, the electric field and the electron multiplication in direct vicinity of a sharp cathode is analysed. The development of the electric field in the pre-breakdown phase of the atmospheric pressure air negative DC corona discharge in the Trichel pulse regime is determined. During the following ultra-fast electrical breakdown, the emission of selected spectral bands of the nitrogen molecule is recorded with high spatiotemporal resolution using the time-correlated single photon counting method. The emission of a Townsend discharge is used to calibrate the setup for the quantitative determination of electric field. Therefore, the Trichel pulse corona and Townsend discharge cell are arranged in the same single-table setup. This direct calibration procedure is described step-by-step including the discussion of known limitations. Finally, the electric field development of the positive streamer passing the 160 μm distance in less than two nanoseconds is determined.Due to the high spatiotemporal gradients of the electric field strength within the streamer breakdown, the local field approximation of the electron component is analysed by investigating numerically the temporal and spatial electron relaxation by means of the solution of the electron Boltzmann equation and Monte Carlo simulation. Results of these computations are given for several reduced electric field values and prove that the electrons are in a hydrodynamic equilibrium state for experimentally given space and time scales for reduced fields above 100 Td.

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The local-mean-energy approximation (LMEA) and the local-field approximation (LFA) are commonly applied to include the electron properties like transport and rate coefficients into a hydrodynamic description of gas discharge plasmas. Both the approaches base on the solution of the stationary spatially homogeneous Boltzmann equation for the electron component, but the consequences of these approaches differ drastically. These consequences of using both the approaches are studied and discussed on a kinetic level and by comparison of results of hydrodynamic investigations of low-pressure glow discharge plasmas. It is found that the LMEA is to be strongly recommended for the application to a hydrodynamic description of dc as well as rf discharge plasmas, while the LFA is conditionally suitable to describe dc glow discharges with rough reaction kinetics only and its application to rf discharge plasmas is inappropriate.

We propose a novel boundary handling algorithm for particle-based fluids. Based on a predictor-corrector scheme for both velocity and position, one- and two-way coupling with rigid bodies can be realized. The proposed algorithm offers significant improvements over existing penalty-based approaches. Different slip conditions can be realized and non-penetration is enforced. Direct forcing is employed to meet the desired boundary conditions and to ensure valid states after each simulation step. We have performed various experiments in 2D and 3D. They illustrate one- and two-way coupling of rigid bodies and fluids, the effects of hydrostatic and dynamic forces on a rigid body as well as different slip conditions. Numerical experiments and performance measurements are provided.