Axisymmetric smoothed particle magnetohydrodynamics

Abstract

Many astrophysical and terrestrial scenarios involving magnetic fields can be approached in axial geometry. Although the smoothed particle hydrodynamics (SPH) technique has been successfully extended to magneto-hydrodynamics (MHD), a well-verified, axisymmetric MHD scheme based on such technique does not exist yet. In this work we fill that gap in the scientific literature and propose and check a novel axisymmetric MHD hydrodynamic code, that can be applied to physical problems which display the adequate geometry. We show that the hydrodynamic code built following these axisymmetric hypothesis is able to produce similar results than standard 3D-SPMHD codes with equivalent resolution but with much lesser computational load.

Smoothed particle magnetohydrodynamics

“…Star formation calculations highlight the preceding limitations. SPMHD calculations that evolve the magnetic field via the induction equation produce magnetically-driven jets and outflows (e.g., Bürzle et al, 2011b;Price et al, 2012;Bate et al, 2014;Tsukamoto et al, 2015b;Lewis et al, 2015;Hopkins and Raives, 2016;Wurster et al, 2018a;Tsukamoto et al, 2018;Wissing and Shen, 2020;García-Senz et al, 2023). However, no such outflows are produced when similar calculations are performed using the Euler potentials (Price and Bate, 2007).…”

“…Additionally, non-ideal MHD formulations for Ohmic dissipation, ambipolar diffusion, and the Hall effect have been constructed (Wurster et al, 2014;Wurster et al, 2016). SPMHD has also been adapted for 2D axisymmetric geometry, promising computational efficiency for phenomena involving magnetic fields with axial geometries (García-Senz et al, 2023).…”

A simple Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics method for fluid flow and heat transfer

“…The violation of the unity condition issue has been also discussed in Lagrangian framework in the presence of shocks and density discontinuities 22–26 . In their studies, they adopted corrected volume terms instead of general volume element ($$$ {V}_{j,t}={m}_{j,0}/{\rho}_{j,t} $$$) to satisfy the unity condition.…”