Despite representing a substantial simplification of the governing equations that describe the behavior magnetized plasmas, fluid models such as extended MHD (XMHD) are still remarkably hard to deal with from an algorithmic standpoint. At the heart of the difficulty is the
multiscale nature of the fluid equations, which support a wide range of temporal and spatial scales. Spatially, XMHD is able to develop very thin layers, whose dynamics may have global impact (e.g., magnetic reconnection). Temporally, XMHD supports fast dispersive waves, with frequencies growing quadratically with the wavenumber. It
also features strong transport anisotropy, with transport along magnetic field lines many orders of magnitude faster than transport perpendicular to them. In this presentation, we will describe efficient, scalable algorithmic strategies to deal with both fast hyperbolic waves and transport anisotropy in XMHD.
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