Structure-preserving operator splitting for 2.5D ideal MHD with an entropy-stable DGSEM and exactly divergence-free compatible finite elements
Abstract
We develop a high-order, fully explicit operator-splitting method for 2.5D ideal magnetohydrodynamics on Cartesian meshes. The hydrodynamic subflow is advanced by an entropy-stable discontinuous Galerkin spectral element method equipped with stagewise oscillation elimination and a positivity-preserving limiter. The magnetic--velocity subflow uses compatible finite elements and mass-lumped reconstructions of electric field and current density. Its discrete-curl update exactly preserves the global H(div) divergence-free subspace, while the ideal semidiscretization balances kinetic, magnetic, and internal energy. Curl-form artificial resistivity and a direction-resolved velocity filter return removed magnetic and kinetic energy to internal energy; consequently, the stabilized magnetic stage preserves positive internal energy and satisfies a discrete entropy inequality. The two solvers are composed by a second-order hydrodynamic--magnetic--hydrodynamic Strang splitting, yielding a matrix-free scheme that retains global mass, nodal admissibility, and magnetic divergence on accepted steps. Smooth Alfvén-wave and advected-vortex tests reveal an even--odd convergence pattern in the magnetic polynomial degree, verify second-order temporal accuracy, and show that stabilization preserves high-order accuracy. Field-loop, Orszag--Tang, rotor, MHD blast-wave, and Kelvin--Helmholtz calculations demonstrate robust performance for nonsmooth multidimensional flows and show that artificial resistivity suppresses grid-scale magnetic oscillations while retaining the resolved structures.
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BibTeX
@misc{fan2026structurepreserving,
title = {{Structure-preserving operator splitting for 2.5D ideal MHD with an entropy-stable DGSEM and exactly divergence-free compatible finite elements}},
author = {Siyuan Fan and Guosheng Fu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10849},
eprint = {2609.10849},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10849},
}
RIS
TY - UNPB
TI - Structure-preserving operator splitting for 2.5D ideal MHD with an entropy-stable DGSEM and exactly divergence-free compatible finite elements
AU - Siyuan Fan
AU - Guosheng Fu
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10849
UR - https://arxiv.org/abs/2609.10849
AB - We develop a high-order, fully explicit operator-splitting method for 2.5D ideal magnetohydrodynamics on Cartesian meshes. The hydrodynamic subflow is advanced by an entropy-stable discontinuous Galerkin spectral element method equipped with stagewise oscillation elimination and a positivity-preserving limiter. The magnetic--velocity subflow uses compatible finite elements and mass-lumped reconstructions of electric field and current density. Its discrete-curl update exactly preserves the global H(div) divergence-free subspace, while the ideal semidiscretization balances kinetic, magnetic, and internal energy. Curl-form artificial resistivity and a direction-resolved velocity filter return removed magnetic and kinetic energy to internal energy; consequently, the stabilized magnetic stage preserves positive internal energy and satisfies a discrete entropy inequality. The two solvers are composed by a second-order hydrodynamic--magnetic--hydrodynamic Strang splitting, yielding a matrix-free scheme that retains global mass, nodal admissibility, and magnetic divergence on accepted steps. Smooth Alfvén-wave and advected-vortex tests reveal an even--odd convergence pattern in the magnetic polynomial degree, verify second-order temporal accuracy, and show that stabilization preserves high-order accuracy. Field-loop, Orszag--Tang, rotor, MHD blast-wave, and Kelvin--Helmholtz calculations demonstrate robust performance for nonsmooth multidimensional flows and show that artificial resistivity suppresses grid-scale magnetic oscillations while retaining the resolved structures.
ER -