Progress, Challenges, and Perspectives of the 3D MHD Numerical Modeling of Oscillations in the Solar Corona

Recent high temporal and spatial resolution satellite observations of the solar corona provide ample evidence of oscillations in coronal structures. The observed waves and oscillations can be used as a diagnostic tool of the poorly known coronal parameters, such as magnetic field, density, and temperature. The emerging field of coronal seismology relies on the interpretation of the various coronal oscillations in terms of theoretically known wave modes, and the comparison of observed and theoretical wave mode properties for the determination of the coronal parameters. However, due to complexity of coronal structures the various modes are coupled, and the application of linear theory of idealized structures to coronal loops and active regions limits the usefulness of such methods. Improved coronal seismology can be achieved by the development of full 3D MHD dynamical model of relevant coronal structures and the oscillation phenomena. In addition to improved accuracy compared to linear analysis, 3D MHD models allow the diagnostic method to include nonlinearity, compressibility, and dissipation. The current progress made with 3D MHD models of waves in the corona is reviewed, and the challenges facing further development of this method are discussed in the perspective of future improvement that will be driven by new high resolution and high cadence satellite data, such as received from Hinode and STEREO, and expected from SDO.