Plasma systems with strong electro-magnetic effects and chemical species transport and reaction occur frequently in nature and are critical for many important technological applications. Examples include stellar interiors, gaseous nebula, the earth's magnetoshpere, and Tokamak and Z-pinch physics. These systems are described by a set of partial differential equations that conserve momentum, mass, charge, and energy for chemical species along with Maxwell's equations for the electric and magnetic fields. The resulting equations are strongly coupled, highly nonlinear, and span a large range of time and length scales, making the scalable, robust, and accurate solution of such systems extremely challenging.

In this presentation, we will discuss the initial development of a new PTR/MHD formulation based on unstructured finite element methods and fully implicit time intergration techniques. Our initial implementation employs a variational multi-scale stabilized finite element solver. We implicitly enforce the div B = 0 constraint by use of a vector potential formulation in 2D and a Helmholtz projection in 3D. We will discuss numerical performance, accuracy, and scalability. Example problems will include fast magnetic reconnection (magnetic island coalescence) and a variety of verification tests some of which leverage the method of manufactured solutions.

*This work was partially funded by the DOE Office of Science AMR Program, and was carried out at Sandia National Laboratories operated for the U.S. Department of Energy under contract no. DE-ACO4-94AL85000