Stable finite elements analysis of viscous dusty plasma

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

Finite element analysis of plasma dust-acoustic waves

For dust acoustic solitary waves, we propose a finite element formulation of the fluid dusty plasma equations. To solve this continuum problem, a Petrov-Galerkin weak form with unwinding is applied. We consider an unmagnetised dusty plasma with negatively charged dust and Boltzmann distributions for electrons and ions. Nonlinearity of electron and ion number density as functions of the electrostatic potential is included. A fully-implicit time-integration is used (backward-Euler method) which requires the derivative of the weak form. A three-field formulation is introduced, with dust number-density, electrostatic potential and dust velocity being the unknown fields. We test the formulation with two numerical (2D and 3D)examples where convergence with mesh size is assessed. These establish the new formulation as a predictive tool in dusty plasmas