Magnetic helicity dissipation and production in an ideal MHD code
  We study a turbulent helical dynamo in a periodic domain by solving the ideal
magnetohydrodynamic (MHD) equations with the FLASH code using the
divergence-cleaning eight-wave method and compare our results with direct
numerical simulations (DNS) using the Pencil Code. At low resolution, FLASH
reproduces the DNS results qualitatively by developing the large-scale magnetic
field expected from DNS, but at higher resolution, no large-scale magnetic
field is obtained. In all those cases in which a large-scale magnetic field is
generated, the ideal MHD results yield too little power at small scales. As a
consequence, the small-scale current helicity is too small compared with that
of the DNS. The resulting net current helicity has then always the wrong sign,
and its statistical average also does not approach zero at late times, as
expected from the DNS. Our results have implications for astrophysical dynamo
simulations of stellar and galactic magnetism using ideal MHD codes.
