Legolas 2.0: Improvements and extensions to an MHD spectroscopic framework

TL;DR

Legolas 2.0 enhances an open-source MHD spectral framework with new features, optimizations, and visualization tools, enabling detailed linear stability analysis and linking it to non-linear phenomena in fluid dynamics.

Contribution

The paper introduces significant extensions to the Legolas code, including subsystem support, performance improvements, and advanced eigenfunction visualization capabilities.

Findings

Improved performance in execution time and memory usage.

Successful visualization of eigenfunctions for instabilities.

Application to Kelvin-Helmholtz and Rayleigh-Taylor instabilities.

Abstract

We report on recent extensions and improvements to the Legolas code, which is an open-source, finite element-based numerical framework to solve the linearised (magneto)hydrodynamic equations for a three-dimensional force- and thermally balanced state with a nontrivial one-dimensional variation. The standard Fourier modes imposed give rise to a complex, generalised non-Hermitian eigenvalue problem which is solved to quantify all linear wave modes of the given system in either Cartesian or cylindrical geometries. The framework now supports subsystems of the eight linearised MHD equations, allowing for pure hydrodynamic setups, only one-dimensional density/temperature/velocity variations, or the option to treat specific closure relations. We discuss optimisations to the internal datastructure and eigenvalue solvers, showing a considerable performance increase in both execution time and memory usage. Additionally the code now has the capability to fully visualise eigenfunctions associated with given wave modes in multiple dimensions, which we apply to standard Kelvin-Helmholtz and Rayleigh-Taylor instabilities in hydrodynamics, thereby providing convincing links between linear stability analysis and the onset of non-linear phenomena.