Projection Methods for Multiscale Problems in Plasma Physics and Applications

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Chorin and Tokman The investigators develop numerical methods that will beeffective in long-time simulations of the multi-scale phenomenaevident in plasma dynamics, particularly in modeling magneticreconnection. They also use the methods in studies of plasmadynamics in the solar corona and in laboratory experiments. Theymake available a software implementation of the methods. Themethods combine projection techniques with schemes of exponentialpropagation type for time-stepping. The dynamical behavior seen in astrophysical and laboratoryplasmas is complicated, and to understand it requires computersimulations. But the phenomena of interest span a wide range oflength and time scales. Consequently, to compute accurately thesolutions of the equations that describe these phenomena,conventional numerical methods require small steps in time oververy long time periods. Similarly, accurate spatial resolution ofthe solutions requires fine spatial meshes. Together, thesefactors require solving very large systems of equations at eachtime step, for a great many time steps. Such calculations areexpensive. The investigators develop and analysze numericalmethods that promise to reduce the computational costs, and applythem to study plasma physics problems. They make the methodsavailable in software. This widens the potential impact of thework, because problems with multiple scales arise in a variety ofscience and engineering applications.