Cross-Code verification and sensitivity analysis to effectively model the electrothermal instability

TL;DR

This paper develops verification cases and compares software frameworks to accurately model electrothermal instability, analyzing the effects of physical parameters on nonlinear growth and providing insights for fluid-based simulation accuracy.

Contribution

It introduces verification cases for ETI modeling and compares different algorithms, highlighting the importance of EOS and vacuum resistivity in nonlinear development.

Findings

Verification cases ensure accurate ETI physics modeling.

Early time agreement in nonlinear ETI simulations with some differences.

EOS and vacuum resistivity are critical parameters for nonlinear ETI evolution.

Abstract

This manuscript presents verification cases that are developed to study the electrothermal instability (ETI). Specific verification cases are included to ensure that the unit physics components necessary to model the ETI are accurate, providing a path for fluid-based codes to effectively simulate ETI in the linear and nonlinear growth regimes. Two software frameworks with different algorithmic approaches are compared for accuracy in their ability to simulate diffusion of a magnetic field, linear growth of the ETI, and a fully nonlinear ETI evolution. The nonlinear ETI simulations show early time agreement, with some differences emerging, as noted in the wavenumber spectrum, late into the nonlinear development of ETI. A sensitivity study explores the role of equation-of-state (EOS), vacuum density, and vacuum resistivity. EOS and vacuum resistivity are found to be the most critical factors in the modeling of nonlinear ETI development.