Projection Methods for Multiscale Problems in Plasma Physics and Applications

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Chorin and Tokman The investigators develop numerical methods that will be effective in long-time simulations of the multi-scale phenomena evident in plasma dynamics, particularly in modeling magnetic reconnection. They also use the methods in studies of plasma dynamics in the solar corona and in laboratory experiments. They make available a software implementation of the methods. The methods combine projection techniques with schemes of exponential propagation type for time-stepping. The dynamical behavior seen in astrophysical and laboratory plasmas is complicated, and to understand it requires computer simulations. But the phenomena of interest span a wide range of length and time scales. Consequently, to compute accurately the solutions of the equations that describe these phenomena, conventional numerical methods require small steps in time over very long time periods. Similarly, accurate spatial resolution of the solutions requires fine spatial meshes. Together, these factors require solving very large systems of equations at each time step, for a great many time steps. Such calculations are expensive. The investigators develop and analysze numerical methods that promise to reduce the computational costs, and apply them to study plasma physics problems. They make the methods available in software. This widens the potential impact of the work, because problems with multiple scales arise in a variety of science and engineering applications.