Application of high-resolution schemes in the modeling of ionization waves in gas discharges

Methods for solving continuity equations are analyzed in application to the modeling of ionization waves in electric discharges in gases. It is shown that the dispersive properties of numerical methods play a key role in the modeling of wave processes. Even when high-resolution schemes are applied, the phase error may lead to substantial distortion of the exponential ionization front, as well as to error in the phase velocity and to a generation of an additional wave whose propagation velocity differs from the phase velocity of the wave. It is proposed to use second order accurate Godunov-type methods, i.e., modified TVD methods. The efficiency of these methods, which are based on monotonized central difference and harmonic mean algorithms, is demonstrated by solving appropriate test problems and by the numerical results obtained for the physical problem of the dynamics of an ionization wave (streamer) at the initial stage of an electric discharge in air.