An asymptotic preserving scheme for the streamer simulation

Mesh dependent stability of discretization of the streamer equations for very high electric fields

“…Moreover the finite volume schemes can manage easily the strong gradients of the ionization fronts. Finally the finite volume schemes fit well in the framework of the asymptotic preserving schemes as has been demonstrated in [18,19] for the Euler equations and, specifically, in [20] for the streamer equations. The asymptotic preserving schemes guarantee good stability performances even when the time integration step is much larger than the plasma relaxation time.…”

“…Let us introduce a simplified version of the streamer model [20,1] when a very high electric field is considered: @ne @t À @ @x n e l e E À Á ¼ al e jEjn e ; dnp dx ¼ al e jEjn e ; dE dx ¼ e e 0 n p À n e À Á ;…”

“…If we compare model (1) with the one proposed in [20,1] we have neglected the negative ions, the recombination terms and the electron attachment.…”

“…(1). In particular, for the solution of the electric field, we have used the asymptotic preserving approach described in [20]. As regards the solution of the evolution equations, for the electrons we have used the stabilized approach described in this paper and for the positive ions we have used an explicit Euler approximation.…”

“…We consider, for the sake of simplicity, a one dimensional model. We concentrate ourselves on the drift-reaction equation with a fixed electric field (the coupling between the electric field solver and the drift equation has been already treated in [18][19][20]). We show that the mesh size plays a crucial role in the stability of finite volume schemes and we propose a stabilization technique that makes them bounded, whatever the mesh size.…”