Stable finite element analysis of viscous dusty plasma. Issue 3 (8th May 2018) - Areias, Pedro; Sikta, Jebun Naher; Pereira dos Santos, Manuel
Abstract : Purpose: The purpose of this paper is to provide an analysis of dust acoustic (solitary) waves including viscosity. Specifically, the authors consider a dusty unmagnetized plasma system consisting of negatively charged dust and Boltzmann electrons and ions. Design/methodology/approach: In this paper, a Petrov–Galerkin weak form with upwinding is adopted. Nonlinearity of ion and electron number density in terms of an electrostatic potential is included. A fully implicit time integration is used (backward Euler method), which requires the first derivative of the weak form. A three-field formulation is proposed, with the dust number density, the electrostatic potential and the dust velocity being the unknown fields. Findings: In this study, two numerical examples are introduced and results show great promise for the proposed formulation as a predictive tool in viscous dusty plasmas. Presence of solitary waves was demonstrated. Dusty plasma vortices are predicted in 2D and 3D, as mentioned in the specialized literature. Research limitations/implications: We observed some dependence on step size, which is due to the simple time-stepping scheme. This can be solved with a higher order integration scheme, which implies an added cost to the solution. Practical implications: Dusty plasmas are found in astrophysics (Saturn rings) and electronics industry at several scales and have high impact as a contaminant. Originality/value: To the authors' knowledge, this is the first paper with a simulation of dusty plasma including vortices.