Implicit and coupled fluid plasma solver with adaptive Cartesian mesh and its applications to non-equilibrium gas discharges

Abstract

We present a new fluid plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (nonlinear, implicit) scheme for non-equilibrium gas discharge plasma. The electrons and ions are described using drift–diffusion approximation coupled to Poisson equation for the electric field. The electron-energy transport equation is solved to account for electron thermal conductivity, Joule heating, and energy loss of electrons in collisions with neutral species. The rate of electron-induced ionization is a function of electron temperature and could also depend on electron density (important for plasma stratification). The ion and gas temperature are kept constant. The transport equations are discretized using a non-isothermal Scharfetter–Gummel scheme to resolve possible large temperature gradients in the sheaths. We demonstrate the new solver for simulations of direct current (DC) and radiofrequency (RF) discharges. The implicit treatment of the coupled equations allows using large time steps. The full-Newton method (FNM) enables fast nonlinear convergence at each time step, offering significantly improved simulation efficiency. We discuss the selection of time steps for solving different plasma problems. The new solver enables solving several problems we could not solve before with existing software: two- and three-dimensional structures of the entire DC discharges including cathode and anode regions, electric field reversals and double-layer formation, the normal cathode spot and an anode ring, moving striations in diffuse and constricted DC discharges, and standing striations in RF discharges. The developed FNM-ACM technique offers many benefits for tackling the disparity of gas discharge plasma systems' time scales and nonlinearity.

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

“…Unfortunately, 3D simulations often use hundreds of millions of grid points [26][27][28] and billions of degrees of freedom. Full Newton methods [54] are not very practical at this scale since the full Jacobian must be factored at every time step. Jacobian-Free Newton-Krylov (JFNK) is a more attractive computational strategy, but it is not clear if JFNK methods remain computationally feasible at this scale, particularly when adaptive mesh refinement (AMR) is required.…”

The principle of minimal power

“…Moving striations in diffuse argon discharges were briefly reported [28] using CFD-ACE+ software, but we could not simulate striations in the constricted discharges due to the strong nonlinearity of the system. The recent development of an implicit and coupled fluid plasma solver [35] made it possible to simulate moving striations in diffuse and constricted DC discharges, [31] and standing striations in CCP [32]. Figure 2 shows an example of calculated moving striations in argon DC discharges at low and high pressures (1 and 400 Torr) in a dielectric tube with a radius of 1 cm and length of 14 cm.…”

“…The fluid models considering the electron thermal conductivity can qualitatively capture the nonlocal effects responsible for the structure of the cathode region in DC discharges [58,59]. The latest models use implicit and coupled solvers with adaptive Cartesian mesh [35] The results of such models shown in figure 8 reproduce the typical structure of DC discharges with the plasma density peak in the negative glow (a), a minimum in the Faraday dark space, an axially constant value in the (striation-free) positive column, and decay near the anode. The two-dimensional electric potential distribution (b) between the equipotential electrodes and a positive column plasma equalizes the electron and ion fluxes to the tube wall.…”

“…Understanding plasma self-organization in the anode region is far from complete. The kinetic and fluid models predict the appearance of a single luminous ring on a solid anode surface [35,65]. The recent model [66] relates the anode spots to the change in the sign of the near-anode voltage.…”

“…Figure 2.Instantaneous distributions of electron density (in 10 10 cm −3 ) in diffuse and constricted DC discharges in a tube of radius 1 cm and length 14 cm at currents near the Pupp boundary. Reproduced from[35]. © IOP Publishing Ltd. All rights reserved.…”