  Very strong magnetic fields can arise in non-central heavy-ion collisions at
ultrarelativistic energies, which may not decay quickly in a conducting plasma.
We carry out relativistic magnetohydrodynamics (RMHD) simulations to study the
effects of this magnetic field on the evolution of the plasma and on resulting
flow fluctuations in the ideal RMHD limit. Our results show that magnetic field
leads to enhancement in elliptic flow for small impact parameters while it
suppresses it for large impact parameters (which may provide a signal for
initial stage magnetic field). Interestingly, we find that magnetic field in
localized regions can temporarily increase in time as evolving plasma energy
density fluctuations lead to reorganization of magnetic flux. This can have
important effects on chiral magnetic effect. Magnetic field has non-trivial
effects on the power spectrum of flow fluctuations. For very strong magnetic
field case one sees a pattern of even-odd difference in the power spectrum of
flow coefficients arising from reflection symmetry about the magnetic field
direction if initial state fluctuations are not dominant. We discuss the
situation of nontrivial magnetic field configurations arising from collision of
deformed nuclei and show that it can lead to anomalous elliptic flow. Special
(crossed body-body) configurations of deformed nuclei collision can lead to
presence of quadrupolar magnetic field which can have very important effects on
the rapidity dependence of transverse expansion (similar to {\it beam focusing}
from quadrupole fields in accelerators).
