Stable finite elements analysis of viscous dusty plasma

Abstract

In the context of analysis of dust acoustic (solitary) waves including viscosity, we introduce a finite elements formulation of the corresponding fluid dust-acoustic wave equations. With this objective, a Petrov-Galerkin weak form with unwinding is adopted. We consider a dusty unmagnetised plasma system consisting of negatively charged dust and Boltzmann electrons and ions. Nonlinearity of ion and electron number density in terms of a 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. Two numerical examples are introduced and results show great promise for the proposed formulation as a predictive tool in viscous dusty plasmas.