  Solar eruptions are the main driver of space-weather disturbances at the
Earth. Extreme events are of particular interest, not only because of the
scientific challenges they pose, but also because of their possible societal
consequences. Here we present a magnetohydrodynamic (MHD) simulation of the 14
July 2000 Bastille Day eruption, which produced a very strong geomagnetic
storm. After constructing a thermodynamic MHD model of the corona and solar
wind, we insert a magnetically stable flux rope along the polarity inversion
line of the eruption's source region and initiate the eruption by boundary
flows. More than 10^33 ergs of magnetic energy are released in the eruption
within a few minutes, driving a flare, an EUV wave, and a coronal mass ejection
(CME) that travels in the outer corona at about 1500 km/s, close to the
observed speed. We then propagate the CME to Earth, using a heliospheric MHD
code. Our simulation thus provides the opportunity to test how well in situ
observations of extreme events are matched if the eruption is initiated from a
stable magnetic-equilibrium state. We find that the flux-rope center is very
similar in character to the observed magnetic cloud, but arrives about 8.5
hours later and about 15 degrees too far to the North, with field strengths
that are too weak by a factor of about 1.6. The front of the flux rope is
highly distorted, exhibiting localized magnetic-field concentrations as it
passes 1 AU. We discuss these properties with regard to the development of
space-weather predictions based on MHD simulations of solar eruptions.
