A static-regridding method for two-dimensional parabolic partial differential equations
Applied Numerical Mathematics
Algorithm 758: VLUGR2: a vectorizable adaptive-grid solver for PDEs in 2D
ACM Transactions on Mathematical Software (TOMS)
Matrix computations (3rd ed.)
How fast the Laplace equation was solved in 1995
Applied Numerical Mathematics
Numerical solution of Fisher's equation using a moving mesh method
Journal of Computational Physics
Stability of Moving Mesh Systems of Partial Differential Equations
SIAM Journal on Scientific Computing
A conservative finite difference method for the mumerical solution of plasma fluid equations
Journal of Computational Physics
Numerical solution of plasma fluid equations using locally refined grids
Journal of Computational Physics
A nested-grid direct Poisson solver for concentrated source terms
Journal of Computational and Applied Mathematics
Numerical simulation of filamentary discharges with parallel adaptive mesh refinement
Journal of Computational Physics
A PIC-MCC code for simulation of streamer propagation in air
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Spatially hybrid computations for streamer discharges: II. Fully 3D simulations
Journal of Computational Physics
Density models for streamer discharges: Beyond cylindrical symmetry and homogeneous media
Journal of Computational Physics
Towards adaptive kinetic-fluid simulations of weakly ionized plasmas
Journal of Computational Physics
Hi-index | 31.48 |
The evolution of negative streamers during electric breakdown of a non-attaching gas can be described by a two-fluid model for electrons and positive ions. It consists of continuity equations for the charged particles including drift, diffusion and reaction in the local electric field, coupled to the Poisson equation for the electric potential. The model generates field enhancement and steep propagating ionization fronts at the tip of growing ionized filaments. An adaptive grid refinement method for the simulation of these structures is presented. It uses finite volume spatial discretizations and explicit time stepping, which allows the decoupling of the grids for the continuity equations from those for the Poisson equation. Standard refinement methods in which the refinement criterion is based on local error monitors fail due to the pulled character of the streamer front that propagates into a linearly unstable state. We present a refinement method which deals with all these features. Tests on one-dimensional streamer fronts as well as on three-dimensional streamers with cylindrical symmetry (hence effectively 2D for numerical purposes) are carried out successfully. Results on fine grids are presented, they show that such an adaptive grid method is needed to capture the streamer characteristics well. This refinement strategy enables us to adequately compute negative streamers in pure gases in the parameter regime where a physical instability appears: branching streamers.