  In this article we describe simulations of Higgs boson production via the
gluon fusion and Higgs-strahlung processes, using the positive weight
next-to-leading-order (NLO) matching scheme, POWHEG, in the Herwig++ 2.3 event
generator. This formalism consistently incorporates the full NLO corrections to
these processes within the parton shower simulation, without the production of
negative weight events. These simulations include a full implementation of the
truncated shower required to correctly model soft emissions in an
angular-ordered parton shower. We present a thorough validation of these
simulations, comparing them to other methods and calculations. The results
obtained for the gluon fusion process corroborate, and provide detailed
explanations for, findings reported by Alioli et al (arXiv:0812.0578) using an
independent POWHEG simulation, neglecting truncated shower effects, released at
the same time as our code.
