Particle based 3D modeling of positive streamer inception

In this report we present a particle based 3D model for the study of streamer inception near positive electrodes in air. The particle code is of the PIC-MCC type and an electrode is included using the charge simulation method. An algorithm for the ada

Improvements for drift-diffusion plasma fluid models with explicit time integration

Drift-diffusion plasma fluid models are commonly used to simulate electric discharges. Such models can computationally be very efficient if they are combined with explicit time integration. This paper deals with two issues that often arise with such models. First, a high plasma conductivity can severely limit the time step. A fully explicit method to overcome this limitation is presented. This method is compared to the existing semi-implicit method, and it is shown to have several advantages. A second issue is specific to models with the local field approximation. Near strong density and electric field gradients, electrons can diffuse parallel to the field, and unphysically generate ionization. Existing and new approaches to correct this behavior are compared. Details on the implementation of the models and the various approaches are provided

Reply to comment on "Improvements for drift-diffusion plasma fluid models with explicit time integration"

This is a reply to the comment of Jiayong Zou on the paper "Improvements for drift-diffusion plasma fluid models with explicit time integration". The criticism in the comment, namely that the current-limited approach is inconsistent with the underlying partial different equations, seems to be invalid. However, this criticism raises an interesting question about the behavior of the current-limited scheme for a given time step, which is discussed in this reply

A geometric multigrid library for quadtree/octree AMR grids coupled to MPI-AMRVAC

We present an efficient MPI-parallel geometric multigrid library for quadtree (2D) or octree (3D) grids with adaptive refinement. Cartesian 2D/3D and cylindrical 2D geometries are supported, with second-order discretizations for the elliptic operators. Periodic, Dirichlet, and Neumann boundary conditions can be handled, as well as free-space boundary conditions for 3D Poisson problems, for which we use an FFT-based solver on the coarse grid. Scaling results up to 1792 cores are presented. The library can be used to extend adaptive mesh refinement frameworks with an elliptic solver, which we demonstrate by coupling it to MPI-AMRVAC. Several test cases are presented in which the multigrid routines are used to control the divergence of the magnetic field in magnetohydrodynamic simulations

The effect of the stochasticity of photoionization on 3D streamer simulations

Positive streamer discharges require a source of free electrons ahead of them for their growth. In air, these electrons are typically provided by photoionization. Here we investigate how stochastic fluctuations due to the discreteness of ionizing photons affect positive streamers in air. We simulate positive streamers between two planar electrodes with a 3D plasma fluid model, using both a stochastic and a continuum method for photoionization. With stochastic photoionization, fluctuations are visible in the streamer's direction, maximal electric field, velocity, and electron density. The streamers do not branch, and we find good agreement between the averaged stochastic results and the results with continuum photoionization. The streamers stay roughly axisymmetric, and we show that results obtained with an axisymmetric model indeed agree well with the 3D results. However, we find that positive streamers are sensitive to the amount of photoionization. When the amount of photoionization is doubled, there is even better agreement between the stochastic and continuum results, but with half the amount of photoionization, stochastic fluctuations become more important and streamer branching starts to occur

A geometric multigrid library for quadtree/octree AMR grids coupled to MPI-AMRVAC

We present an efficient MPI-parallel geometric multigrid library for quadtree (2D) or octree (3D) grids with adaptive refinement. Cartesian 2D/3D and cylindrical 2D geometries are supported, with second-order discretizations for the elliptic operators. Periodic, Dirichlet, and Neumann boundary conditions can be handled, as well as free-space boundary conditions for 3D Poisson problems, for which we use an FFT-based solver on the coarse grid. Scaling results up to 1792 cores are presented. The library can be used to extend adaptive mesh refinement frameworks with an elliptic solver, which we demonstrate by coupling it to MPI-AMRVAC. Several test cases are presented in which the multigrid routines are used to control the divergence of the magnetic field in magnetohydrodynamic simulations

3D Spatially hybrid model for streamer discharge

Streamers are rapidly growing plasma filaments. They play an important role in the early stages of lightning and, as well as in industrial application such as lighting, plasma assisted combustion and disinfection. In previous work, the first generation of 3D spatially hybrid codes was developed by Chao Li, to study the propagation of negative streamer without photoionization in a background field above the break-down value[1-2]. We now have set up the second generation codes to improve and optimize the original program, and to make it accessible. Adaptive Mesh Refinement and parallel computing technique are being adopted as well, to increase the accuracy, efficiency and parameter range of simulations. The codes are being used to study the streamers emergence from the inception cloud, streamers branching and feather formation in different N2:O2 ratios, and streamers interaction. [1]C. Li et al., J. Comput. Phys. 231, 1020 (2012); [2]C. Li et al., Plasma Sources Sci. Technol.(submitted), preprint: http://arxiv.org/abs/1203.503

Towards user-friendly, public domain simulations of the precursor of lightning: streamers

Streamers play an important role in the early stages of lightning and can be directly seen as sprite discharges. Many kinds of streamer discharge models developed at CWI are presented, using Particle-in-cell/Monte Carlo, fluid and hybrid codes from 1D to 3D. The codes are being improved and documented currently, to make them user-friendly and available on internet for potential users

Geometric multigrid method for solving Poisson's equation on octree grids with irregular boundaries

A method is presented to include irregular domain boundaries in a geometric multigrid solver. Dirichlet boundary conditions can be imposed on an irregular boundary defined by a level set function. Our implementation employs quadtree/octree grids with adaptive refinement, a cell-centered discretization and pointwise smoothing. Boundary locations are determined at a subgrid resolution by performing line searches. For grid blocks near the interface, custom operator stencils are stored that take the interface into account. For grid block away from boundaries, a standard second-order accurate discretization is used. The convergence properties, robustness and computational cost of the method are illustrated with several test cases. New version program summary: Program Title: Afivo CPC Library link to program files: https://doi.org/10.17632/5y43rjdmxd.2 Developer's repository link: https://github.com/MD-CWI/afivo Licensing provisions: GPLv3 Programming language: Fortran Journal reference of previous version: Comput. Phys. Commun. 233 (2018) 156–166. https://doi.org/10.1016/j.cpc.2018.06.018 Does the new version supersede the previous version?: Yes. Reasons for the new version: Add support for internal boundaries in the geometric multigrid solver. Summary of revisions: The geometric multigrid solver was generalized in several ways: a coarse grid solver from the Hypre library is used, operator stencils are now stored per grid block, and methods for including boundaries via a level set function were added. Nature of problem: The goal is to solve Poisson's equation in the presence of irregular boundaries that are not aligned with the computational grid. It is assumed these irregular boundaries are defined by a level set function, and that a Dirichlet type boundary condition is applied. The main applications are 2D and 3D simulations with octree-based adaptive mesh refinement, in which the mesh frequently changes but the irregular boundaries do not. Solution method: A geometric multigrid method compatible with octree grids is developed, using a cell-centered discretization and point-wise smoothing. Near irregular boundaries, custom operator stencils are stored. Line searches are performed to locate interfaces with sub-grid resolution. To increase the methods robustness, this line search is modified on coarse grids if boundaries are otherwise not resolved. The multigrid solver uses OpenMP parallelization