Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations
MetadataShow full item record
Type of Work15 pages
Citation of Original PublicationHudson, Joshua; Jolly, Michael; Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations; Journal of Computational Dynamics, 2019, 6 (1) : 131-145; http://dx.doi.org/10.3934/jcd.2019006
RightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
We study the computational efficiency of several nudging data assimilation algorithms for the 2D magnetohydrodynamic equations, using varying amounts and types of data. We find that the algorithms work with much less resolution in the data than required by the rigorous estimates in . We also test other abridged nudging algorithms to which the analytic techniques in  do not seem to apply. These latter tests indicate, in particular, that velocity data alone is sufficient for synchronization with a chaotic reference solution, while magnetic data alone is not. We demonstrate that a new nonlinear nudging algorithm, which is adaptive in both time and space, synchronizes at a super exponential rate.