Validation of Data-driven Boundaries for MHD Simulations of Flux Emergence and Solar Eruptions

Data-driving methods that can directly utilize the wealth of photospheric observations from modern solar observatories as a boundary condition to numerical simulations are, in principle, highly promising tools for studying the physics of flux emergence leading to eruptions. In practice it is a challenging task to utilize observational data for this purpose in a way that is both faithful to the observations and consistent with the underlying evolution of the simulation. We here present an optimization method capable of surmounting these obstacles by using Singular Value Decomposition to find a characteristics-based representation of the MHD equations that are solved self consistently with the observational data. As a first validation of our method, we extract data from a ground truth MHD simulation of an expanding spheromak and use them to data-drive a series of smaller simulations at a range of synthetic observational cadences. As a second validation, we remove the information about the temporal evolution of mass and energy density and compare the performance of our method against a more typical MHD data-driving approach that assumes these properties are constant in time. Our method performs well in all of these tests, and as such is ready to be presented with real observational data.