  We investigate the effect of large magnetic fields on the $2+1$ dimensional
reduced-magnetohydrodynamical expansion of hot and dense nuclear matter
produced in $\sqrt{s_{\rm NN}}$ = 200 GeV Au+Au collisions. For the sake of
simplicity, we consider the case where the magnetic field points in the
direction perpendicular to the reaction plane. We also consider this field to
be external, with energy density parametrized as a two-dimensional Gaussian.
The width of the Gaussian along the directions orthogonal to the beam axis
varies with the centrality of the collision. The dependence of the magnetic
field on proper time ($\tau$) for the case of zero electrical conductivity of
the QGP is parametrized following [Deng 2012], and for finite electrical
conductivity following [Tuchin 2013]. We solve the equations of motion of ideal
hydrodynamics for such an external magnetic field. For collisions with non-zero
impact parameter we observe considerable changes in the evolution of the
momentum eccentricities of the fireball when comparing the case when the
magnetic field decays in a conducting QGP medium and when no magnetic field is
present. The elliptic-flow coefficient $v_2$ of $\pi^{-}$ is shown to increase
in the presence of an external magnetic field and the increment in $v_2$ is
found to depend on the evolution and the initial magnitude of the magnetic
field.
