A conservative MHD scheme on unstructured Lagrangian grids for Z-pinch hydrodynamic simulations

Wu, Feiyang; Ramis, R.; Li, Zhenghong

doi:10.1016/j.jcp.2017.12.014

Cited by 16 publications

(7 citation statements)

References 36 publications

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“…However, the Lagrangian description, where the computational mesh follows the motion of the plasma, is preferred for the applications of interest as mentioned in the introduction (section 1). The proper transformation of the coordinates to the fluid frame gives rise to the Lagrangian formulation [7]:…”

Section: Lagrangian Magneto-hydrodynamicsmentioning

confidence: 99%

“…However, energy conservation was not considered. This work continues along this line, applying the recent formalism of [7], in order to formulate a conserving and consistent multi-dimensional high-order curvilinear finite element method for MHD. Flexibility and scalability of the numerical implementation are provided by the MFEM library [8,9].…”

Section: Introductionmentioning

confidence: 99%

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Lagrangian Magneto-Hydrodynamics Based On Curvilinear Finite Elements

Nikl¹,

Kuchařík²,

Weber³

2021

14th WCCM-ECCOMAS Congress

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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.

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Section: Lagrangian Magneto-hydrodynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lagrangian Magneto-Hydrodynamics Based On Curvilinear Finite Elements

Nikl¹,

Kuchařík²,

Weber³

2021

14th WCCM-ECCOMAS Congress

View full text Add to dashboard Cite

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“…Its dynamics is modeled by the Euler equations, which are complemented by Faraday's law for the self-consistent magnetic field B. In the Lagrangian formulation, they take the following integral form [3]:…”

Section: Physical Modelmentioning

confidence: 99%

“…We are particularly interested in the Lagrangian approach, where the coordinate system follows the flow of the fluid. It is mostly favored in areas of modeling where the medium undergoes extreme compression or expansion like inertial confinement fusion [1,2], Z-pinches [3], supernovae collapses [4], cosmic jets [5], prepulse effects of ultra-intense lasers [6,7] or laser ion acceleration beamlines [8,9,10] as are explored at facilities like ELI Beamlines [11,12] and other multi-PW laser systems worldwide [13].…”

Section: Introductionmentioning

confidence: 99%

“…However, conservative time stepping was still limited to the second order only and formulation of MHD was missing. Later, a convenient formulation of conservative Lagrangian MHD was developed for the staggered discretization [3]. Although limited to the second order and only to the transverse component of the magnetic field in 2D, the methodology is compatible with the finite element hydrodynamics.…”

Section: Introductionmentioning

confidence: 99%

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High-Order Curvilinear Finite Element Magneto-Hydrodynamics I: A Conservative Lagrangian Scheme

Nikl,

Kuchařík,

Weber

2021

Preprint

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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. In this paper, a multi-dimensional conservative high-order resistive magneto-hydrodynamic 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. 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.

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