Lagrangian magneto-hydrodynamics based on curvilinear finite elements

0566137 - ÚFP 2023 RIV ES eng C - Konferenční příspěvek (zahraniční konf.)
Nikl, Jan - Kuchařík, M. - Weber, S.
Lagrangian magneto-hydrodynamics based on curvilinear finite elements.
14th WCCM-ECCOMAS Congress 2020. Barcelona: International Center for Numerical Methods in Engineering, 2021 - (Chinesta, F.; Abgrall, R.; Allix, O.; Kaliske, M.; Néron, D.), Roč. 300 (2021), s. 186-192. ISSN 2696-6999.
[14th WCCM-ECCOMAS Congress 2020. online (ES), 11.01.2021-15.01.2021]
Grant CEP: GA ČR(CZ) GA19-24619S
Institucionální podpora: RVO:61389021
Klíčová slova: Finite element method * Isoparametric elements * Lagrangian hydrodynamics * Magnetic diffusion * Magneto-hydrodynamics
Obor OECD: Fluids and plasma physics (including surface physics)
https://www.scipedia.com/public/Nikl_et_al_2021a

The magneto-hydrodynamic model is widely used for description of magnetized fluids in plasma dynamics, microfluidics, astrophysics and many other applications. In terms of modelling, the Lagrangian formulation is favourable for the rapid expansion during laser–target interaction for example. This is the case for inertial fusion and laboratory astrophysics applications, which are our primary interest. However, the proposed numerical method remains general and can be applied elsewhere. The conservation properties and divergence-free magnetic field are crucial aspects, which are not satisfied by the traditional numerical schemes. Here, the Lagrangian hydrodynamics using curvilinear finite elements is extended to the resistive magneto-hydrodynamics. An energy-conserving numerical scheme is formulated maintaining divergence-free magnetic field. The mixed finite element formulation provides theoretically arbitrary order of the spatial convergence and application on unstructured Lagrangian grids in multiple dimensions. An example of a physically relevant numerical simulation is presented.
Trvalý link: https://hdl.handle.net/11104/0337571