A novel numerical scheme for nonlinear electron-plasma oscillations

TL;DR

This paper introduces a high-order finite volume numerical scheme using CWENO4 reconstruction and Runge-Kutta time integration to accurately simulate nonlinear electron-plasma oscillations, validated through stability and convergence tests.

Contribution

It presents a new, easy-to-implement fourth-order scheme for nonlinear plasma oscillation analysis, improving accuracy and stability over existing methods.

Findings

The scheme accurately reproduces known plasma oscillation results.

It demonstrates negligible numerical dissipation over long simulation times.

The method confirms fourth-order convergence through error analysis.

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 solving electron fluid equations numerically. The present method employs a fourth-order accurate centrally weighted essentially nonoscillatory reconstruction (CWENO4) 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. The fourth-order accuracy of the existing approach is also confirmed by evaluating the convergence of errors for the nonlinear electron plasma oscillations in a cold non-dissipative plasma.