Arago's disk — Welcome to LS-DYNA Examples

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A bar magnet is suspended above an aluminum disk. When the disk starts spinning, it will ‘drag’ the magnet and cause it to start spinning in the same direction albeit at a lower speed. The effect was discovered by François Arago in 1824. The method used here is a monolithic FEM-BEM approach available in the latest versions of LS-DYNA’s EM solver.

Description

A bar magnet is suspended above an aluminum disk. When the disk starts spinning, it will ‘drag’ the magnet and cause it to start spinning in the same direction albeit at a lower speed. The effect was discovered by François Arago in 1824. At the time of their discovery, Arago’s rotations were surprising effects that were difficult to explain. 200 years later, thanks to simulation, those effects can be studied in depth. The method used here is a monolithic FEM-BEM approach available in the latest versions of LS-DYNA’s EM solver. The fringes show streamlines of Eddy current generated in the disk.

Keywords

```*CONTROL_TERMINATION
*CONTROL_TIMESTEP
*DATABASE_BINARY_D3PLOT
*DEFINE_CURVE_TITLE
*EM_CIRCUIT
*EM_CONTROL
*EM_CONTROL_COUPLING
*EM_CONTROL_TIMESTEP
*EM_MAT_001
*EM_MAT_002
*EM_OUTPUT
*EM_PERMANENT_MAGNET
*EM_SOLVER_BEM
*EM_SOLVER_BEMMAT
*EM_SOLVER_FEM
*EM_SOLVER_FEMBEM_MONOLITHIC
*END
*KEYWORD
*MAT_RIGID
*PARAMETER
*PART
*SECTION_SOLID
*TITLE```

Reduced Input

```\$-----------------------------------------------------------------------------
\$
\$ Example provided by Iñaki (LSTC)
\$
\$
\$
\$X------------------------------------------------------------------------------
\$X
\$X 1. Run file as is.
\$X    Requires LS-DYNA MPP Dev dated March 2021 (or more recent) with double precision
\$X
\$X------------------------------------------------------------------------------
\$# UNITS: (kg/m/s)
\$X------------------------------------------------------------------------------
*KEYWORD
*EM_CONTROL
\$    emsol
1                                                           2         2
*EM_CONTROL_TIMESTEP
\$#  tstype    dtcons      lcid
1    0.0005
*EM_CONTROL_COUPLING
,2
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
\$                                                                              \$
\$                             EM CIRCUIT                                       \$
\$                                                                              \$
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
*EM_PERMANENT_MAGNET
\$--------1---------2---------3---------4---------5---------6---------7---------8
\$       ID   Part ID         -     North     South         M=0.38/mu0
1         1                   1         2      1.e6
\$         1         1                   1         2 302394.39
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
\$                                                                              \$
\$                             EM MAT and EOS                                   \$
\$                                                                              \$
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
\$*EM_MAT_001
\$\$   em_mid     mtype     sigma       eos
\$         1         2      1.e7
*EM_MAT_002
\$ Magnetic material 1
\$      mid     mtype     sigma     eosid     murel     eosmu
1         2      1.e5         0      1.11
\$         1         2        0.                1.11
*EM_MAT_001
\$   em_mid     mtype     sigma       eos
3         4      6.e7
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
\$                                                                              \$
\$                             EM SOLVER                                        \$
\$                                                                              \$
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
*EM_SOLVER_BEMMAT
\$#   matid                                                                reltol
1                                                                  1e-8
*EM_SOLVER_BEMMAT
\$#   matid                                                                reltol
2                                                                  1e-8
*EM_SOLVER_BEMMAT
\$#   matid                                                                reltol
3                                                                  1e-8
*EM_SOLVER_FEMBEM_MONOLITHIC
\$--------1---------2---------3---------4---------5---------6---------7---------8
\$ COUPLING  KSP_TYPE  KSP_ATOL  KSP_RTOL KSP_MAXIT GMRES_RST               DEBUG
0              1.e-12     1.e-4    100000
\$,,1.e-20,1.e-5
\$,1.e-9
\$--------1---------2---------3---------4---------5---------6---------7---------8
\$NEWT_STOL NEWT_ATOL NEWT_RTOL NEWT_MAXI
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
\$                                                                              \$
\$                             EM OUTPUT                                        \$
\$                                                                              \$
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
*EM_OUTPUT
\$     matS      matF      solS      solF      mesh
2         2         2         2         0
*END```