  Strange mode instabilities in the envelopes of massive stars lead to shock
waves, which can oscillate on a much shorter timescale than that associated
with the primary instability. The phenomenon is studied by direct numerical
simulation using a, with respect to time, implicit Lagrangian scheme, which
allows for the variation by several orders of magnitude of the dependent
variables. The timestep for the simulation of the system is reduced appreciably
by the shock oscillations and prevents its long term study. A procedure based
on domain decomposition is proposed to surmount the difficulty of vastly
different timescales in various regions of the stellar envelope and thus to
enable the desired long term simulations. Criteria for domain decomposition are
derived and the proper treatment of the resulting inner boundaries is
discussed. Tests of the approach are presented and its viability is
demonstrated by application to a model for the star P Cygni. In this
investigation primarily the feasibility of domain decomposition for the problem
considered is studied. We intend to use the results as the basis of an
extension to two dimensional simulations.
