High-order curvilinear finite element magneto-hydrodynamics I: A conservative Lagrangian scheme

0560134 - ÚFP 2023 RIV US eng J - Journal Article
Nikl, Jan - Kuchařík, M. - Weber, S.
High-order curvilinear finite element magneto-hydrodynamics I: A conservative Lagrangian scheme.
Journal of Computational Physics. Roč. 464, September (2022), č. článku 111158. ISSN 0021-9991. E-ISSN 1090-2716
R&D Projects: GA MŠMT EF16_019/0000778; GA ČR(CZ) GA19-24619S
Institutional support: RVO:61389021
Keywords : Conservative methods * Curvilinear meshes * Finite element method * High-order methods * Lagrangian hydrodynamics * Resistive magneto-hydrodynamics
OECD category: Fluids and plasma physics (including surface physics)
Impact factor: 4.1, year: 2022
Method of publishing: Limited access
https://www.sciencedirect.com/science/article/pii/S0021999122002200?via%3Dihub

Magneto-hydrodynamics is one of the foremost models in plasma physics with applications in inertial confinement fusion, astrophysics and elsewhere. Advanced numerical methods are needed to get an insight into the complex physical phenomena. The classical Lagrangian methods are typically limited to the low orders of convergence and suffer from violation of the divergence-free condition for magnetic field or conservation of the invariants. This paper is the first part of a new series about high-order non-ideal magneto-hydrodynamics, where a multi-dimensional conservative Lagrangian method based on curvilinear finite elements is presented. The condition on zero divergence of magnetic field and conservation of mass, momentum, magnetic flux and the total energy are satisfied exactly. The curvilinear elements prevent entangling of the computational mesh and its imprinting into the solution. A high-order conservative time integration is applied, where an arbitrary order of convergence is attained for problems of ideal magneto-hydrodynamics. The resistive magnetic field diffusion is solved by an implicit scheme. Description of the method is given and multiple test problems demonstrating properties of the scheme are performed. The construction of the method and possible future directions of development are discussed.
Permanent Link: https://hdl.handle.net/11104/0333152