New Criteria for Mesh Adaptation in Finite Volume Simulation of Planar Ionization Wavefront Propagation

Abstract Adaptive unstructured finite volume methods for ionization waves are receiving increased attention mainly because of their ability to provide a flexible spatial discretization. Hence, some areas can be resolved in great detail while not over-resolving other areas. Our purpose is to examine the numerical performance of a new criteria for mesh adaptation which account only for the elliptic equation for the electric potential. The proposed adaptive finite volume method has important advantages in the discretization of the gradient fluxes and diffusion terms using unstructured grids and satisfies the conservation property. Numerical results are presented for a propagation of ionization waves in a rectangular domain.