A spectral/hp element MHD solver

TL;DR

This paper introduces a spectral/hp element MHD solver based on Nektar++, demonstrating high accuracy and convergence in simulating Hartmann and Hunt flows, with applications in stability analysis.

Contribution

The paper presents a novel spectral/hp element MHD solver integrated with Nektar++, enabling precise simulations of MHD flows and stability assessments.

Findings

Achieved exponential convergence in simulations.

Numerical accuracy up to 10^{-12} for flow states.

Stability eigenvalues accurate to 10^{-5}.

Abstract

A new MHD solver, based on the Nektar++ spectral/hp element framework, is presented in this paper. The velocity and electric potential quasi-static MHD model is used. The Hartmann flow in plane channel and its stability, the Hartmann flow in rectangular duct, and the stability of Hunt's flow are explored as examples. Exponential convergence is achieved and the resulting numerical values were found to have an accuracy up to $10^{-12}$ for the state flows compared to an exact solution, and $10^{-5}$ for the stability eigenvalues compared to independent numerical results.