Eigenvalue Method for NEI Unit in FLASH Code

Abstract

We describe an improved non-equilibrium ionization (NEI) method that we have developed as an optional module for the FLASH magnetohydrodynamic simulation code. The method employs an eigenvalue approach rather than the earlier iterative ODE approach to solve the stiff differential equations involved in NEI calculations. The new code also allows the atomic data to be easily updated from the AtomDB database. We compare both the updated atomic data and the methods separately. The new atomic data are shown to make a significant difference in some circumstances, although the general trends remain the same. Additionally, the new method also allows simultaneous calculation of the non-equilibrium radiative cooling, which is not included in the original method. The eigenvalue method improves the calculation efficiency overall with no loss of accuracy. We explore some common ways to present the non-equilibrium ionization state with a sample simulation, and find that using average ionic charge difference from the equilibrium tends to be the clearest method.

Nonequilibrium Ionization Modeling of Petschek-type Shocks in Reconnecting Current Sheets in Solar Eruptions

“…Orlando et al (2003) investigated the effects of NEI in the compact flare loop by combining the NEI calculation within the hydrodynamic (HD) modeling. An NEI solver (Zhang et al 2018) using the eigenvalue method (e.g., Masai 1984;Hughes & Helfand 1985;Smith & Hughes 2010) and the AtomDB database (Foster et al 2018) has been developed to perform fast NEI calculations in the FLASH code (Fryxell et al 2000), and has been used to analyze the NEI in supernova remnants (e.g., Zhang et al 2019). Charge states in the solar wind have been calculated using the plasma electron temperature, density, and velocity in several solar wind simulations such as the Michigan Ionization Code model (e.g., Landi et al 2012;Landi & Lepri 2015) and Magnetohydrodynamic Algorithm outside a Sphere model (e.g., Lionello et al 2019).…”