Efficient Computational Model for Inductive Plasma Flows

A new approach to the numerical modeling of inductive plasmas is presented. The governing magnetohydrodynamic equations are discretized in a second-order accurate finite volume manner. A straightforward pressure-stabilized flow field solver is introduced as an alternative to the staggered-mesh solvers used in traditional algorithms. It is argued that the widely used integral boundary formulation for the electric field is computationally expensive and cannot be incorporated into an efficient iterative solution procedure. This approach is abandoned in favor of a 'far field' formulation of the electric field, such that powerful iterative methods can be applied to speed up the calculation. The discretized equations are solved through a damped Picard method and an approximate and full Newton method. Efficient linear algebra methods are used to solve the linear systems arising from the iterative methods. An appropriate linearization of the strongly positive Joule heating source term is important for the convergence at the linear level. The new model is tested on an LTE argon inductive plasma computation. The proposed approximate Newton method is found to converge substantially better than the Picard method. The full Newton method appears promising, although its successful use on fine meshes still requires improvements to the linear solver used.