  The nonlinear dynamics of outflows driven by magnetic explosion on the
surface of a compact star is investigated through special relativistic
magnetohydrodynamic simulations. We adopt, as the initial equilibrium state, a
spherical stellar object embedded in hydrostatic plasma which has a density
$\rho(r) \propto r^{- \alpha}$ and is threaded by a dipole magnetic field. The
injection of magnetic energy at the surface of compact star breaks the
equilibrium and triggers a two-component outflow. At the early evolutionary
stage, the magnetic pressure increases rapidly around the stellar surface,
initiating a magnetically driven outflow. A strong forward shock driven outflow
is then excited. The expansion velocity of the magnetically driven outflow is
characterized by the Alfv\'en velocity on the stellar surface, and follows a
simple scaling relation $v_{\rm mag} \propto {v_{\rm A}}^{1/2}$. When the
initial density profile declines steeply with radius, the strong shock is
accelerated self-similarly to relativistic velocity ahead of the magnetically
driven component. We find that it evolves according to a self-similar relation
$\Gamma_{\rm sh} \propto r_{\rm sh}$, where $\Gamma_{\rm sh}$ is the Lorentz
factor of the plasma measured at the shock surface $r_{\rm sh}$. Purely
hydrodynamic process would be responsible for the acceleration mechanism of the
shock driven outflow. Our two-component outflow model, which is the natural
outcome of the magnetic explosion, can provide a better understanding of the
magnetic active phenomena on various magnetized compact stars.
