Simulating the Photospheric to Coronal Plasma Using Magnetohydrodynamic Characteristics. I. Data-driven Boundary Conditions

Abstract

We develop a general description of how information propagates through a magnetohydrodynamic (MHD) system based on the method of characteristics and use that to formulate numerical boundary conditions that are intrinsically consistent with the MHD equations. Our formulation includes two major advances for simulations of the Sun. First, we derive data-driven boundary conditions that optimally match the state of the plasma inferred from a time series of observations of a boundary (e.g., the solar photosphere). Second, our method directly handles random noise and systematic bias in the observations, and finds a solution for the boundary evolution that is strictly consistent with MHD and maximally consistent with the observations. We validate the method against a Ground Truth (GT) simulation of an expanding spheromak. The data-driven simulation can reproduce the GT simulation above the photosphere with high fidelity when driven at high cadence. Errors progressively increase for lower driving cadence until a threshold cadence is reached and the driven simulation can no longer accurately reproduce the GT simulation. However, our characteristic formulation of the boundary conditions still requires adherence of the boundary evolution to the MHD equations even when the driven solution departs from the true solution in the driving layer. That increasing departure clearly indicates when additional information at the boundary is needed to fully specify the correct evolution of the system. The method functions even when no information about the evolution of some variables on the lower boundary is available, albeit with a further decrease in fidelity.

Exact Nonlinear Decomposition of Ideal-MHD Waves Using Eigenenergies

“…Indeed, such a description forms the basis of many numerical MHD methods (Harten et al 1983), and a (linear) version has been used to identify waves in solar wind observations (Zank et al 2023). Recently, Tarr et al (2024) demonstrated how the characteristic description of MHD could be used to locally decompose and reconstruct the dynamical evolution of an MHD system in terms of these fully nonlinear characteristic modes. While those authors focused on using the formalism to properly implement BCs, they suggested that the method is underutilized for the analysis of simulations, particularly for the unsolved problem of tracking the propagation and interaction of MHD waves in simulations.…”