A novel numerical scheme for nonlinear electron plasma oscillations

Abstract

In this work, we suggest an easy-to-code higher-order finite volume semi-discrete scheme to analyze the nonlinear behavior of the electron-plasma oscillations by the direct numerical simulation of electron fluid equations. The present method employs a fourth-order accurate centrally weighted essentially nonoscillatory reconstruction polynomial for estimating the numerical flux at the grid-cell interfaces, and a fourth-order Runge-Kutta method for the time integration. The numerical implementation is validated by reproducing earlier results for both non-dissipative and dissipative cold plasmas. The stability of the present scheme is illustrated by evolving the nonlinear electron plasma oscillations in a cold non-dissipative plasma for hundred plasma periods, which also display a negligible numerical dissipation. Moreover, the fourth-order accuracy of the existing approach is confirmed by evaluating the convergence of errors for nonlinear electron plasma oscillations in a cold non-dissipative plasma.