  We introduce a new Rigid-Field Hydrodynamics approach to modeling the
magnetospheres of massive stars in the limit of very-strong magnetic fields.
Treating the field lines as effectively rigid, we develop hydrodynamical
equations describing the 1-dimensional flow along each, subject to pressure,
radiative, gravitational, and centrifugal forces. We solve these equations
numerically for a large ensemble of field lines, to build up a 3-dimensional
time-dependent simulation of a model star with parameters similar to the
archetypal Bp star sigma Ori E. Since the flow along each field line can be
solved for independently of other field lines, the computational cost of this
approach is a fraction of an equivalent magnetohydrodynamical treatment.
  The simulations confirm many of the predictions of previous analytical and
numerical studies. Collisions between wind streams from opposing magnetic
hemispheres lead to strong shock heating. The post-shock plasma cools initially
via X-ray emission, and eventually accumulates into a warped, rigidly rotating
disk defined by the locus of minima of the effective (gravitational plus
centrifugal) potential. But a number of novel results also emerge. For field
lines extending far from the star, the rapid area divergence enhances the
radiative acceleration of the wind, resulting in high shock velocities (up to
~3,000 km/s) and hard X-rays. Moreover, the release of centrifugal potential
energy continues to heat the wind plasma after the shocks, up to temperatures
around twice those achieved at the shocks themselves. Finally, in some
circumstances the cool plasma in the accumulating disk can oscillate about its
equilibrium position, possibly due to radiative cooling instabilities in the
adjacent post-shock regions.
