An axisymmetric unstructured finite volume method applied to the numerical modeling of an atmospheric pressure gas discharge

We develop a finite volume method based on unstructured triangular and/or quadrangular meshes for the numerical modeling of gas discharges at atmospheric pressure. The discretization of the computational domain is performed with median-dual control-volumes. Gradient calculations at the faces of the control-volumes are based on finite-element interpolation using shape functions. An FCT method was chosen for the species transport integration. The accuracy of the numerical scheme is verified for different types of mesh-elements in a plane-to-plane DBD geometry. We present comparisons with literature results based on the immersed boundary method in a point-to-plane geometry and investigate the need of a high-order scheme for an accurate model of a filamentary discharge. Finally, we apply our scheme in a study of a discharge between two hemispherical electrodes covered with dielectrics, while focusing on sufficient spatial resolution in the vicinity of the dielectric surface.