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.
*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
$-----------------------------------------------------------------------------
$
$ 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
