A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift-diffusion equations and the computation of electric field. The proposed numerical method provides a time-space accuracy control of the solution, and thus, an effective accurate resolution independent of the fastest physical time scale. An important improvement of the computational efficiency is achieved whenever the required time steps go beyond standard stability constraints associated with mesh size or source time scales for the resolution of the drift-diffusion equations, whereas the stability constraint related to the dielectric relaxation time scale is respected but with a second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate the propagation of highly nonlinear ionizing waves as streamer discharges, as well as highly multi-scale nanosecond repetitively pulsed discharges, describing consistently a broad spectrum of space and time scales as well as different physical scenarios for consecutive discharge/post-discharge phases, out of reach of standard non-adaptive methods.Comment: Support of Ecole Centrale Paris is gratefully acknowledged for several month stay of Z. Bonaventura at Laboratory EM2C as visiting Professor. Authors express special thanks to Christian Tenaud (LIMSI-CNRS) for providing the basis of the multiresolution kernel of MR CHORUS, code developed for compressible Navier-Stokes equations (D\'eclaration d'Invention DI 03760-01). Accepted for publication; Journal of Computational Physics (2011) 1-2

Adaptive multiresolution computations applied to detonations

A space-time adaptive method is presented for the reactive Euler equations describing chemically reacting gas flow where a two species model is used for the chemistry. The governing equations are discretized with a finite volume method and dynamic space adaptivity is introduced using multiresolution analysis. A time splitting method of Strang is applied to be able to consider stiff problems while keeping the method explicit. For time adaptivity an improved Runge--Kutta--Fehlberg scheme is used. Applications deal with detonation problems in one and two space dimensions. A comparison of the adaptive scheme with reference computations on a regular grid allow to assess the accuracy and the computational efficiency, in terms of CPU time and memory requirements.Comment: Zeitschrift f\"ur Physicalische Chemie, accepte

A comparison of 3D particle, fluid and hybrid simulations for negative streamers

In the high field region at the head of a discharge streamer, the electron energy distribution develops a long tail. In negative streamers, these electrons can run away and contribute to energetic processes such as terrestrial gamma-ray and electron flashes. Moreover, electron density fluctuations can accelerate streamer branching. To track energies and locations of single electrons in relevant regions, we have developed a 3D hybrid model that couples a particle model in the region of high fields and low electron densities with a fluid model in the rest of the domain. Here we validate our 3D hybrid model on a 3D (super-)particle model for negative streamers in overvolted gaps, and we show that it almost reaches the computational efficiency of a 3D fluid model. We also show that the extended fluid model approximates the particle and the hybrid model well until stochastic fluctuations become important, while the classical fluid model underestimates velocities and ionization densities. We compare density fluctuations and the onset of branching between the models, and we compare the front velocities with an analytical approximation

Runaway electrons from a ‘beam-bulk’ model of streamer: application to TGFs

International audienc

Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures

A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator splitting, finite volume adaptive multiresolution and high order time integrators with specific stability properties for each operator, this strategy yields high computational efficiency for large multidimensional computations on standard architectures such as powerful workstations. However, the data structure of the original implementation, based on trees of pointers, provides limited opportunities for efficiency enhancements, while posing serious challenges in terms of parallel programming and load balancing. The present contribution proposes a new implementation of the whole set of numerical methods including Radau5 and ROCK4, relying on a fully different data structure together with the use of a specific library, TBB, for shared-memory, task-based parallelism with work-stealing. The performance of our implementation is assessed in a series of test-cases of increasing difficulty in two and three dimensions on multi-core and many-core architectures, demonstrating high scalability

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

The physics of streamer discharge phenomena

In this review we describe a transient type of gas discharge which is commonly called a streamer discharge, as well as a few related phenomena in pulsed discharges. Streamers are propagating ionization fronts with self-organized field enhancement at their tips that can appear in gases at (or close to) atmospheric pressure. They are the precursors of other discharges like sparks and lightning, but they also occur in for example corona reactors or plasma jets which are used for a variety of plasma chemical purposes. When enough space is available, streamers can also form at much lower pressures, like in the case of sprite discharges high up in the atmosphere. We explain the structure and basic underlying physics of streamer discharges, and how they scale with gas density. We discuss the chemistry and applications of streamers, and describe their two main stages in detail: inception and propagation. We also look at some other topics, like interaction with flow and heat, related pulsed discharges, and electron runaway and high energy radiation. Finally, we discuss streamer simulations and diagnostics in quite some detail. This review is written with two purposes in mind: First, we describe recent results on the physics of streamer discharges, with a focus on the work performed in our groups. We also describe recent developments in diagnostics and simulations of streamers. Second, we provide background information on the above-mentioned aspects of streamers. This review can therefore be used as a tutorial by researchers starting to work in the field of streamer physics.Comment: 89 pages, 29 figure

The physics of streamer discharge phenomena

In this review we describe a transient type of gas discharge which is commonly called a streamer discharge, as well as a few related phenomena in pulsed discharges. Streamers are propagating ionization fronts with self-organized field enhancement at their tips that can appear in gases at (or close to) atmospheric pressure. They are the precursors of other discharges like sparks and lightning, but they also occur in for example corona reactors or plasma jets which are used for a variety of plasma chemical purposes. When enough space is available, streamers can also form at much lower pressures, like in the case of sprite discharges high up in the atmosphere. We explain the structure and basic underlying physics of streamer discharges, and how they scale with gas density. We discuss the chemistry and applications of streamers, and describe their two main stages in detail: inception and propagation. We also look at some other topics, like interaction with flow and heat, related pulsed discharges, and electron runaway and high energy radiation. Finally, we discuss streamer simulations and diagnostics in quite some detail. This review is written with two purposes in mind: First, we describe recent results on the physics of streamer discharges, with a focus on the work performed in our groups. We also describe recent developments in diagnostics and simulations of streamers. Second, we provide background information on the above-mentioned aspects of streamers. This review can therefore be used as a tutorial by researchers starting to work in the field of streamer physics