Implicit Integration and Constraint Preservation in Resistive MHD Fusion Modeling

Fusion holds the promise of a clean, sustainable and safe energy source for the future. While research in this field has been ongoing for the last half century, much work remains before it may prove a viable source of energy. In this talk, I introduce some of the scientific and engineering challenges remaining in fusion energy, and the role of applied mathematics research in overcoming these obstacles. In particular, I will discuss the resistive magnetohydrodynamics model used to study fusion stability and refueling. For this model, I investigate the use of implicit time-discretization techniques and the ensuing nonlinear methods required for their solution. Through analysis of these algorithms, we then discuss preservation of the solenoidal constraint on the magnetic field, and introduce some model improvements to better preserve such properties of the discrete solution.