The Virtual Element Method for the 3D Resistive Magnetohydrodynamic model
Louren\c{c}o Beir\~ao da Veiga, Franco Dassi, Gianmarco Manzini,, Lorenzo Mascotto
TL;DR
This paper introduces a novel four-field Virtual Element Method for 3D resistive Magnetohydrodynamics that ensures divergence-free velocity and magnetic fields, validated through convergence analysis and numerical tests.
Contribution
It develops a new VEM discretization for 3D MHD equations on polyhedral meshes with proven divergence-free properties and convergence analysis.
Findings
Method guarantees divergence-free velocity and magnetic fields.
Convergence analysis confirms method's accuracy.
Numerical tests validate theoretical results.
Abstract
We present a four-field Virtual Element discretization for the time-dependent resistive Magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete formulation. The proposed method employs general polyhedral meshes and guarantees velocity and magnetic fields that are divergence free up to machine precision. We provide a full convergence analysis under suitable regularity assumptions, which is validated by some numerical tests.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Electromagnetic Simulation and Numerical Methods · Superconducting Materials and Applications