Magnetohydrodynamic modeling of solar magnetic arcades using exponential propagation methods

Details Magnetohydrodynamic modeling of solar magnetic arcades using exponential propagation methods Magnetohydrodynamic modeling of solar magnetic arcades using exponential propagation methods

Oct 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001phdt.........8t&link_type=abstract

Thesis (PhD). CALIFORNIA INSTITUTE OF TECHNOLOGY, Source DAI-B 62/04, p. 1897, Oct 2001, 178 pages.

Computer Science

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1

Scientific paper

Advanced numerical methods based on exponential propagation have been applied to magnetohydrodynamic (MHD) simulations. This recently developed numerical technique evolves the system of nonlinear equations using exponential propagation of the Jacobian matrix. The exponential of the matrix is approximated by projecting it onto the Krylov subspace using the Arnoldi algorithm. The primary advantage of the exponential propagation method is that it allows time steps exceeding the Courant-Friedrichs-Lewy (CFL) limit. Another important aspect is faster convergence of the iteration computing the Krylov subspace projection compared to solving an implicit formulation of the system with similar iterative methods. Since the time scales in the resistive MHD equations are widely separated the exponential propagation methods are especially advantageous for computing the long term evolution of a low-beta plasma. We analyze several types of exponential propagation methods, highlight important issues in the development of such techniques and discuss their implementation and performance. In the second part of this work we present numerical MHD models which describe the evolution of the magnetic arcades in the solar corona. We first validate our approach by demonstrating application of the exponential schemes to two existing magnetohydrodynamic models. We simulate the reconnection process resulting from shearing the footpoints of two-dimensional magnetic arcades and compute the three-dimensional linear force-free states of plasma configurations. The final chapter of this work is dedicated to a new three-dimensional numerical model of the dynamics of coronal plasma configurations. The model is motivated by observations and laboratory experiments simulating the evolution of solar arcades. We analyze the results of numerical simulations and demonstrate that our numerical approach provides an accurate and stable way to compute the solution to the zero-β resistive MHD system. Based on comparisons of the simulation results and the observational data we offer an explanation for the observed structure of eruptive events in the corona called coronal mass ejections (CME). We argue that diversity of the images of CMEs obtained by the observational instruments can be explained as two- dimensional projections of a unique three-dimensional plasma configuration and suggest an eruption mechanism.

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