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

• Some discretizations of the streamer problem may be unstable.
• The instability is caused by the advection–reaction terms when the mesh is too coarse.
• A stabilization is proposed and analyzed.
• The new scheme is stable whatever mesh is used.

The simulation of streamer evolution has many technological applications ranging from pollution reduction to surface treatments. In this paper we study an instability that may affect the discretized form of the streamer model when a very high electric field is considered and when a representative finite volume method is used. It is shown that the instability is caused by the advection–reaction terms that represent the transport and the production of electrons. It is proved that the mesh spacing greatly affects the properties of the discrete method in terms of stability and accuracy. A stabilization technique is introduced and tested. The proposed method is effective even when coarse meshes are used.