Plasma Modeling: Methods and Applications by Gianpiero Colonna Antonio D’Angola

Author:Gianpiero Colonna, Antonio D’Angola
Language: eng
Format: epub
ISBN: 9780750312004
Publisher: IOP Publishing
Published: 2016-12-24T00:00:00+00:00

(7.72)

Introducing equation (7.72) in equation (7.71) and applying a weighted residual approach we obtain the weak formulation of the electrodynamic problem:

(7.73)

A linear algebraic system is obtained using the shape functions in as a weighting function W:

(7.74)

The system (7.74) has to be defined and solved at each time step. Great attention therefore needs to be paid to optimizing the solution of this system, as poor performance of the electrodynamic solver would dramatically impair the overall efficiency of the whole code. We can observe in equation (7.27) that the Hall parameter determines the anisotropy of the conductivity tensor . Thus the anisotropy of the electrodynamics is more pronounced for high values of the electron mobility. These conditions may be expected in plasmas at relatively low pressure and density, as in MHD aerospace applications in the hypersonic regimes of interest. An ILU-type preconditioned GMRES solver has been adopted for the solution of equation (7.74). The convergence of the solver can become very critical for high values of the Hall parameters in the plasmas, and high-quality preconditioning is needed in order to enhance the performance. A relatively straightforward way to obtain a higher accuracy in preconditioning is to perform a convenient numbering of the mesh nodes. In [29] the authors report a reverse Cuthill–McKee ordering weighted on the local direction of the magnetic induction field with respect to the topology of the triangular mesh utilized.

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