Characteristics of dust-ion-acoustic shock in inhomogeneous plasma by WENO scheme simulation

Based on the hydrodynamic equations, the characteristics of nonlinear dust-ion-acoustic shock propagation in an inhomogeneous dusty plasma are numerically studied, by means of the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme. The inhomogeneous dust charging process for different plasma parameters has been incorporated and its effect on the shock propagation has been investigated. Comparisons of the shocks in the cases of different ion density distributions and different electron-to-ion density ratios are presented. The results show that the dust charging process results in wave damping and dissipation, and the decrease of the electron-to-ion density ratio leads to the increase of the speed, amplitude and width of the shock front. Moreover, the dispersion effect is dominant in the case of sharp shocks whereas the smooth shocks are easily dissipated