HIGH ORDER EULERIAN SCHEMES FOR FLUID MODELLING OF STREAMER DYNAMICS

摘要

The streamer dynamics in corona discharges is governed by the classical fluid transport equations for conservation of density, momentum transfer and energy of charged particles coupled to the field equation. Due to the high spatio-temporal density gradients and the strong coupling between transport and field equations, specific cares have to be taken into account for the numerical solution of such equations. The high order Piecewise Parabolic Method (PPM) is used for the first time in the case of the streamer dynamic modelling. Its efficiency, in terms of computing time and Absolute Error, is compared with other classical high order numerical schemes already used in streamer modelling as the Superbee Monotone Upstreamcentred Scheme for Conservation Law (MUSCL), the ETBFCT algorithm (Flux Corrected Transport technique) and the Zalesak FCT algorithm including the peak preserver condition. The scheme comparisons and validations are firstly undertaken using a periodic mathematic test (Davies test) having an analytical solution that transports a compressible density square wave in a stationary and oscillating velocity field. The Davies test well reproduces the streamer head behaviour with steep density gradients in sharp velocity field variations. The numerical solutions are analyzed as a function of the period number, the spatial resolution and the Courant-Friedrich-Lewy (CFL) number. In all tested cases, the PPM scheme shows the best efficiency. Then the comparison is performed in the framework of a classical 1.5D streamer model better adapted for the present parametric studies than a cylindrical 2D model. The efficiency and behaviour of the four tested numerical schemes are analyzed through a converged PPM solution obtained at high spatial resolution.