An immersed boundary method to simulate positive streamer propagationin point-to-plane geometry in air

摘要

This paper presents the application of the immersed boundary method, initially developed in fluid mechanics, tothe simulation of streamer discharge in point-to-plane geometry. First the use of an immersed boundary methodto solve the Poisson's equation is presented and discussed. To validate the method, the potential calculated for anhyperboloid electrode over a plane is compared to the analytical potential. Then the use of an immersedboundary method to solve drift-diffusion equations for charged species is presented and discussed. In both cases,'ghost points' (cell points in the electrodes) are used to take into account the boundary condition at the edge ofthe hyperboloid electrode. The immersed boundary method has been coupled to a 1D adaptive mesh refinementtechnique to simulate efficiently the discharge propagation in centimeter gaps. Finally, results obtained on thepropagation of a positive streamer discharge between a hyperboloid anode and a plane cathode in air atatmospheric pressure are presented.