Stable finite element analysis of viscous dusty plasma

Abstract

PurposeThe 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/approachIn 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.FindingsIn 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/implicationsWe 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 implicationsDusty plasmas are found in astrophysics (Saturn rings) and electronics industry at several scales and have high impact as a contaminant.Originality/valueTo the authors’ knowledge, this is the first paper with a simulation of dusty plasma including vortices.