Effective Algorithms for Temporally Stiff Magneto-Fluid Problems

Dalton Schnack

Long time scale numerical simulations of hot, dense, highly magnetized plasmas require the application of a magneto-fluid model. One such
mathematical description is resistive MHD. While this model is known to be limited for predicting the details of the dynamics of advanced
fusion plasmas, it contains many of the features of more precise descriptions, and can serve as an effective paradigm for developing and
testing algorithms for the solutions of the more advanced models. All of these models exhibit an extreme separation of time scales, or temporal stiffness, that dictates the use of implicit methods of temporal discretization. A fully implicit solution of the non-linear
equations may be too costly to obtain solutions using reasonable computing resources. Semi-implicit methods, which are equivalent to
operator splitting, allow the offending fast time scales to be isolated and treated implicitly and accurately, often with little more effort
than is required for a linearized problem. These methods have become mature and widely used in computational treatments of the resistive MHD
model in both space and fusion settings, and can serve as a guide for developing stable, efficient algorithms for the long time scale solution of more precise fluid models. Algorithms and examples of semi-implicit methods applicable to both resistive and extended MHD are given.

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