Development of SUPG and Stabilized Finite Element Method Solvers for the Two Fluid Plasma Model

This dissertation describes efforts to employ stabilized finite element method approaches to simulate ideal two fluid plasma dynamics. First, the streamline-upwind/Petrov-Galerkin (SUPG) finite element method, which is well developed and known to be applicable to models containing terms like those in the ideal two fluid plasma model, is employed. Then, in an attempt to address some shortcomings found in that approach, another stabilized finite element method is developed along similar lines, starting from a steady state advection-reaction equation rather than a steady state advection-diffusion equation as was done in the development of the SUPG method. The performance of the SUPG method for the ideal two fluid plasma model is evaluated by simulating the two fluid analog of the Brio-Wu shock tube problem and the Geospace Environment Modeling (GEM) challenge problem, one dimensional and two dimensional transient problems, respectively. The stabilized method based on an advection-reaction equation is ultimately applied to the two fluid analog of the Brio-Wu shock tube problem after some examination in the context of simpler models.

The SUPG finite element method was found to perform well for the two fluid analog of the Brio-Wu shock tube problem at lower charge to mass ratios, but some difficulty was encountered at higher charge to mass ratios. It is possible that this difficulty could be resolved with more grid resolution. The advection-reaction equation based stabilized method was able to simulate the two fluid analog of the Brio-Wu shock tube problem, but ultimately did not appear to be superior to existing methods such as the SUPG finite element method.